当前位置:首页 > 学术报告 > 偏微分方程中心学术报告

2013年
报告题目: Hopf Bifurcation in Semilinear Equations with Non-dense Domain with Applications to the Transmission Dynamics of Influenza
报 告 人: Prof. Shigui Ruan,University of Miami, USA
时间地点: 2013年10月18日上午10:00 S1013
摘       要: Influenza viruses infect about 5 million people and cause about 500,000 deaths each year around the world, the reasons for the seasonal influenza epidemics are still not clear. The H7N9 avian influenza A virus caused high mortality rate in China in 2013. Understanding the transmission dynamics of influenza will be very helpful in designing successful vaccine programs and introducing public health interventions. There are two types of changes in influenza A viruses: antigenic drift which occurs all the time and causes the annual influenza epidemics and antigenic shift which happens only occasionally but causes pandemics.
In this talk, I will present an age-structured type evolutionary epidemiological model of influenza A drift, in which the susceptible class is continually replenished because the pathogen changes genetically and immunologically from one epidemic to the next, causing previously immune hosts to become susceptible. Applying our recent established center manifold theory for semilinear equations with non-dense domain, I show that Hopf bifurcation occurs in the model. This demonstrates that the age-structured type evolutionary epidemiological model of influenza A drift has an intrinsic tendency to oscillate due to the evolutionary and/or immunological changes of the influenza viruses.
I will also briefly talk about modeling the H1N1 influenza A pandemic in 2009 and the H7N9 avian influenza A outbreak in China in 2013.
报告题目: The inverse problem for a cavity with interior measurements
报 告 人: 秦海华 博士,中国矿业大学数学系,江苏徐州
时间地点: 2013年9月13日下午4:30 S703
摘       要: In contrast to the typical inverse scattering problems where the measurements are in the exterior of the objects, in this talk we consider an inverse scattering problem of reconstructing the shape and the surface impedance of a cavity from a knowledge of measured scattered fields on a curve inside the cavity due to point sources placed on the same curve. We apply a regularized Newton-type method to solve our inverse problem and give several numerical examples to show the feasibility of the method.
报告题目: A Bocher theorem for conformally invariant degenerate elliptic equations
报 告 人: Prof.Yanyan Li,Rutgers University, USA
时间地点: 2013年9月4日上午9:00 S1013
摘       要:  
报告题目: Post Galerkin Methods Based on an Approximate Inertial Manifold
报 告 人: 黄艾香教授,西安交通大学数学与统计学院
时间地点: 2013年8月16日上午10:00 S1013
摘       要: In this talk we shall present several new domain decomposition methods for solving some linear and nonlinear inverse problems. The motivations and derivations of the methods will be discussed, and numerical experiments will be demonstrated.
报告题目: Some Efficient Domain Decomposition Methods for a Class of Inverse Problems
报 告 人: Professor Jun Zou,Dept of Math, Chinese University of Hong Kong
时间地点: 2013年8月15日下午4:30 S712
摘       要: In this talk we shall present several new domain decomposition methods for solving some linear and nonlinear inverse problems. The motivations and derivations of the methods will be discussed, and numerical experiments will be demonstrated.
报告题目: IBVP for Boussinesq system with nonlinear heat diffusion
报 告 人: Prof. Ronghua Pan,Georgia Institute of Technology, USA
时间地点: 2013年8月12日下午4:00 S1013
摘       要: On a bounded 2D domain with smooth boundary, we prove the global existence of a unique smooth solution to the inviscid heat conductive Boussinesq Equations with nonlinear diffusion, along with homogeneous Dirichlet boundary for temperature and slip boundary for velocity. Such a solution is also shown as vanishing viscosity limit for the corresponding viscous and heat conductive Boussinesq equation with the same boundary condition for temperature, and Navier boundary condition for the velocity. This talk is based on the joint work with Huapeng Li, Hongjun Yuan, and Weizhe Zhang.
报告题目: Compressible Navier-Stokes Approximation of the Boltzmann Equation
报 告 人: Prof. Huijiang Zhao,Wuhan University
时间地点: 2013年7月26日上午10:30 S712
摘       要: Even though the system of the compressible Navier-Stokes equations is not a limiting system of the Boltzmann equation when the Knudsen number tends to zero, it is the second order approximation by applying the Chapman-Enskog expansion. The purpose of this talk, which is based on a recent work joint with Dr. S.-Q. Liu and Prof. T. Yang, is to justify this approximation rigorously in mathematics. That is, if the difference between the initial data for the compressible Navier-Stokes equations and the Boltzmann equation is of the second order of the Knudsen number, so is the difference between two solutions for all time. The analysis is based on a refined energy method for a fluid-type system using the techniques for the system of viscous conservation laws.
报告题目: Well-posedness of the Boltzmann Equation in General Settings
报 告 人: Prof. Tong Yang,City University of Hong Kong
时间地点: 2013年7月26日上午9:30 S712
摘       要: The existence of classical solutions to the Cauchy problem for the Boltzmann equation without angular cutoff has been extensively studied in the framework when the solution has Maxwellian decay in the velocity variable. In this talk, we will present some recent progress on some cases in more general settings.
报告题目: Monotonicity Formula Approach to Some Supercritical Elliptic Problems
报 告 人: Prof. Juncheng Wei,The Chinese University of Hong Kong
时间地点: 2013年7月25日上午10:00 S712
摘       要: We use monotonicity formula and some geometric ideas to obtain regularity and classification of solutions for supercritical problems of second and fourth order problems. In particular, we obtain the optimal Holder estimate for second order MEMS problems with negative exponents and optimal Joseph-Lundgren exponent for finite Morse (positive or sign changing) solutions of fourth order supercritical problems. (Joint work with J. Davila, L. Dupaigne and Kelei Wang)
报告题目: The interaction between free flow in conduit and porous media flow
报 告 人: Prof. Xiaoming Wang,The Florida State University,USA
时间地点: 2013年7月22日上午10:00 S1013
摘       要: Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton membrane exchange fuel cell, multiphase flows in conduits and in porous media must be considered together. The description of the interaction between free flow in conduit/channel interact with flow in porous media is a challenge.
In this talk we present a family of phase field models that couples two-phase flow in conduit with two-phase flow in porous media. These models together with the associated interface boundary conditions are derived utilizing Onsager's extremum principle. The models derived enjoy physically important energy law. Numerical scheme that preserves the energy law will be presented as well.
报告题目: Parabolic limits of first order nonlinear hyperbolic equations
报 告 人: Prof. Yue-Jun Peng,Université Blaise Pascal, France
时间地点: 2013年7月11日下午4:00 S712
摘       要: In this talk, I present recent results on singular limits of first order nonlinear hyperbolic equations with stiff relaxation term in several space dimensions. The limit equations are of parabolic type accompanied by differential constraints. I give physical models to explain this limit. The justification of the limit is shown in a framework of smooth local in time solutions under stability conditions.
报告题目: Bubbling Solutions for Chern-Simons Model in a Torus
报 告 人: Prof. Shusen Yan,University of New England, Australia
时间地点: 2013年7月5日上午11:00 S1013
摘       要:  
报告题目: Some analytic results on the Ericksen-Leslie system modeling nematic liquid crystal flows
报 告 人: Prof. Changyou Wang,University of Kentucky, USA
时间地点: 2013年7月5日上午10:00 S1013
摘       要: In this talk, I will discuss some recent works on the hydrodynamic flow of nematic liquid crystal materials, namely the Ericksen-Leslie system. This includes local and global well-posedness for rough initial data in three dimensions, and the existence and uniqueness of global weak solutions to the general Ericksen-Leslie system in dimension two.
报告题目: Existence of seven solutions for a semilinear Dirichlet problem
报 告 人: Prof. Alfonso Castro,Harvey Mudd College, USA
时间地点: 2013年6月17日下午4:00 S1013
摘       要:  
报告题目: On a model of the Kompaneets equation and Bose-Einstein condensation
报 告 人: Prof. Hailiang Liu,Iowa State University, USA
时间地点: 2013年6月14日上午10:30 S1013
摘       要: We study the Kompaneets equation with an aim to understand a phenomenon related to Bose-Einstein condensation which appears during the process of relaxation to equilibrium for the photon energy distribution. This talk is concerned with a model for the Kompaneets equation with the spontaneous scattering term dropped, posed on a bounded interval. Uniqueness of a large class of weak solutions with initial data of finite moments is established, together with a proven moment stability and comparison principle. Existence of the global weak solution is proved via a regularized problem subject to an additional linear boundary condition at origin. Bose-Einstein condensation is shown to form in finite time when initial photon number is above a threshold value. Below this threshold a condensate will develop for some initial data, but not for others. Large time convergence to equilibrium solutions is established, with convergences rates obtained for some special data. This is a joint work with D. Levermore and R. Pego.
报告题目: An eigenvalue method using multiple frequency data for inverse scattering problems
报 告 人: Prof. Jiguang Sun,Dept of Math, Michigan Tech University, USA
时间地点: 2013年6月6日下午3:00 C110
摘       要:

Dirichlet, Neumann, and transmission eigenvalues have important applications in qualitative methods in inverse scattering. Motivated by the fact that these eigenvalues can be obtained from scattering data, we propose an eigenvalue method using multiple frequency data. The method detects eigenvalues and builds indicator functions to reconstruct the support of the target. Numerical reconstruction is quite satisfactory.

We provide some preliminary analysis for the special case of circular object.

报告题目: Regularized transformation-optics cloaking in acoustic and electromagnetic scattering
报 告 人: Prof. Hongyu Liu,Dept of Math, University of North Carolina at Charlotte, USA
时间地点: 2013年6月7日下午4:00 C110
摘       要: In this talk, I will describe the recent theoretical and computational progress on our work on regularized transformation-optics cloaking. Ideal cloak makes use of singular metamaterials, posing much challenge for practical realization. Regularization is incorporated into the construction in order to avoid the singular structures.
报告题目: Decay property for symmetric hyperbolic systems with non-symmetric relaxation
报 告 人: Prof. Yoshihiro Ueda,Faculty of Maritime Sciences, Kobe University, Japan
时间地点: 2013年5月22日下午4:00 S1013
摘       要: The results of this talk are based on a joint work with Shuichi Kawashima (Kyushu University) and Renjun Duan (Chinese University of Hong Kong).In this talk, we consider the Cauchy problem for the first-order linear symmetrichyperbolic system of equations with relaxation. For this general linear degenerately dissipative system it is interesting to study its decay structure under additional conditions on the coefficient matrices and further investigate the corresponding time-decay property of solutions to the Cauchy problem. When the degenerate relaxation matrix is symmetric, Umeda-Kawashima-Shizuta proved the large-time asymptotic stability of solutions for a class of equations of hyperbolic-parabolic type with applications to both electromagneto-fluid dynamics and magnetohydrodynamics. The key idea that first introduced the so-called Kawashima-Shizuta condition is to design the compensating matrix to capture the dissipation of systems over the degenerate kernel space of the relaxation matrix. The typical feature of the time-decay property of solutions established in those work is that the high frequency part decays exponentially while the low frequency part decays polynomially with the rate of the heat kernel. Unfortunately, when the degenerate relaxation matrix is not symmetric, that results can not be applied any longer. In fact, this is the case for some concrete systems, for example, the Timoshenko system and the Euler-Maxwell system, where the linearized relaxation matrix indeed has a nonzero skew-symmetric part while it was still proved that solutions decay in time in some different way. Therefore, our purpose of this talk is to formulate some new structural conditions in order to extend the previous works to our general system when the relaxation matrix is not symmetric, which can include both the Timoshenko system and the Euler-Maxwell system.
报告题目: Gevrey regularity of subelliptic Monge-Ampère equations in the plane
报 告 人: 陈化 教授,武汉大学
时间地点: 2013年5月9日下午4:00 S712
摘       要:  
报告题目: A new approach to error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
报 告 人: 李步扬 博士,香港城市大学数学系, 南京大学数学系
时间地点: 2013年3月22日上午10:30 S709
摘       要:  
报告题目: A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature
报 告 人: Prof.Yanyan Li,Rutgers University, USA
时间地点: 2013年3月19日下午4:30 S1013
摘       要:  
报告题目: 任意运动目标的脉冲电磁散射模拟与应用
报 告 人: 夏明耀 教授,电子科技大学电子工程学院
时间地点: 2013年2月28日下午4:00 思源楼1013
摘       要: 超高声速空天目标的探测与识别,是国家当前的重大需求。这类目标还经常伴随旋转和尾迹等复杂问题。雷达目标的探测与识别基于目标散射特性,但是通过实测方式获得散射特性成本高昂甚至根本不可能。使用计算电磁学方法对其进行模拟,并利用仿真数据进行相关的成像与识别方法研究,是必然选择。
本讲座介绍超高声速运动目标的脉冲电磁散射特性模拟方法。与以往基于"停--走--停"的准静止方式不同 (它只适用于低速运动情况,即在雷达脉冲与目标作用时间内目标移动的距离远小于载波波长),我们的方法完全基于相对论时空变换和电磁场变换,即爱因斯坦所称的"框架跳跃法",可以对任意运动形式目标的瞬态散射特性进行模拟分析,包括目标质心的超高声速匀速或加速平动运动和绕目标质心的自旋、章动和锥旋等微动运动。进一步讨论利用仿真数据分析运动形式对目标距离像的影响,目标回波与SAR/ISAR成像模拟,目标散射特征提取与识别方法,目标的多普勒和微多普勒特征提取方法,运动目标识别方法等问题。
简       历: 夏明耀,博士,电子科技大学教授,博士生导师,教育部长江学者特聘教授,国家杰出青年基金获得者,IEEE高级会员。1988~2002年在中科院电子所工作,在此期间在英国牛津大学和香港城市大学工作三年;2002年加入北京大学信息科学技术学院,历任副教授、教授和应用电子学所所长;2010年调入电子科技大学。中国计算物理学会计算电磁学分会副主任委员、《电波科学学报》编委,多种国际刊物审稿人,多次担任国际/地区学术会议技术委员会主席/副主席或委员。主要研究领域包括计算电磁学与应用、微波电路与天线、微波遥感理论与建模。主持国家级科研项目10余项,发表论文150多篇,获得过国际无线电联盟(URSI)青年科学家奖和中国科学院自然科学一等奖。
报告题目: Algebraization and Exact Solution of a Master Hamiltonian of Spins and Bosons
报 告 人: Prof. Yao-Zhong Zhang,The University of Queensland
时间地点: 2013年1月8日上午11:00 晨兴中心110
摘       要: We introduce novel polynomial deformations of the 3-dimensional A1 algebra, which give rise to an algebraization of a very general Hamiltonian of interest in atomic, molecular, nuclear and optical physics. We construct the unitary representations and the corresponding differential operator realizations of the polynomial algebras. This enables us to transform the Hamiltonian into a higher order differential operator which is quasi-exactly solvable. We solve the Hamiltonian differential equation by the functional Bethe ansatz, thus obtaining the exact solutions of the general Hamiltonian. This includes as special cases solutions of many interesting models such as the Bose-Einstein condensate models, the Lipkin-Meshkov-Glick model and the Tavis-Cummings model.
2012年
报告题目: Optimal Onofri inequality on surfaces
报 告 人: Prof. Marcello Lucia,The City University of New York
时间地点: 2012年12月27日上午10:00 晨兴中心110
摘       要: On the sphere, Onofri obtained an optimal inequality for a Moser-Trudinger type functional. For more general surfaces, or for functions on a disk that are invariant under a group of rotations, I will show that a similar inequality holds.
报告题目: Modeling and numerical methods for an inverse problem arising from genetic regulatory network identification
报 告 人: Professor Xiaobing Feng,Department of Mathematics, The University of Tennessee, USA
时间地点: 2012年11月19日上午10:00 思源楼S1013
摘       要: Understanding gene regulatory networks at the system level is a fundamental issue in the post-genomic era. Recent advances in genome sequencing and emerging high-throughput technologies, such as DNA and protein chips and microarray technology, enable parallel measurement of the spatial-temporal expression levels of thousands of genes or proteins simultaneously. It has opened up great possibilities and opportunities to unveil gene regulatory networks at the large scale. One of fundamental and difficult questions in systems biology is what information each genome or gene map encodes.
Decoding genomes and making use of the discovered information has been the main focus of the post-genomic research and of systems biology. In this talk I shall first introduce both deterministic and stochastic differential equation (DE) based mathematical models for reverse engineering genetic regulatory networks which only use genomic information provided by microarray data. I shall then present a novel variational DE-modeling framework and efficient numerical methods for solving the resulted reverse engineering genetic regulatory network models. Finally, I shall also present some model validation results using both synthetic datasets and real world microarray datasets of E. Coli and Yeast.
报告题目: 多解计算的一类间接增广牛顿法
报 告 人: 谢资清 教授,湖南师范大学数学与计算机科学学院
时间地点: 2012年11月16日上午10:00 思源楼S712
摘       要:  
报告题目: Boundary Relations for Hyperbolic-Dissipative Systems
报 告 人: 刘太平 教授,中研院院士,台湾"中央"研究院数学研究所
时间地点: 2012年11月14日下午4:00 思源楼S712
摘       要:  
报告题目: 退化双曲方程弱解的存在性
报 告 人: 王振 研究员,中科院武汉物理与数学研究所
时间地点: 2012年10月24日下午4:00 思源楼S703
摘       要:  
 
报告题目: Elastic Scattering by Diffraction Gratings and Rough Surfaces
报 告 人: Dr. Johannes Elschner,Weierstrass Institute Berlin, Germany
时间地点: 2012年10月15日上午10:30 思源楼S1013
摘       要: The first part of the talk reviews joint work with Guanghui Hu on elastic scattering by (non-smooth) periodic surfaces. Using a variational approach, solvability results are established for the boundary value problems of the first, second, third and fourth kind. The second part presents new results (joint with G. Hu) on elastic scattering by a 2D unbounded rough surface. Existence and uniqueness of solutions at arbitrary frequency is proved applying a variational approach and a priori estimates for the Navier equation.
报告题目: Energy (non)-dissipation for the Boussinesq system
报 告 人: Professor Lorenzo Brandolese,Institut Camille Jordan, University Lyon 1, France
时间地点: 2012年9月18日下午4:00 思源楼S1013
摘       要:  
报告题目: Passive tracer dynamics
报 告 人: Prof. Szymon Peszat,Polish Academy of Sciences and Technical University of Krakow
时间地点: 2012年8月10日下午2:30 思源楼S712
摘       要:  
报告题目: Energy-Conserved S-FDTD Schemes for Maxwell's Equations
报 告 人: Professor Dong Liang,Dept of Math & Statistics, York University, Toronto, Canada
时间地点: 2012年8月9日下午4:00 思源楼S712
摘       要: Computational electromaganetics has been playing a more and more important role in many areas of electromagnetic industry, such as radio frequency, microwave, integrated optical circuits, antennas, and wireless engineering. In lossless medium, the energies of electromagnetic waves keep constant for all time. Physically keeping the invariance of energies in time is important in computation of Maxwell's equations and specially in a long term computation of electromagnetic fields. In this talk, I will introduce energy-conserved identities of Maxwell's equations and will present our newly developed energy-conserved S-FDTD schemes for Maxwell's equations in two or three dimensions. Theoretical analysis and numerical experiments will also be presented to show the efficiency of the developed schemes.
报告题目: Stochastic Partial Differential Equations
报 告 人: Prof. Szymon Peszat,Polish Academy of Sciences and Technical University of Krakow
时间地点: 2012年8月7-8日上午9:30 思源楼S703
摘       要:  
报告题目: Boundary Regularity for the Steady Stokes Type Flow with Shear Thickening Viscosity
报 告 人: Prof. Hyeong-Ohk, Bae,Ajou University, Korea
时间地点: 2012年7月19日下午3:00 思源楼S1013
摘       要:  
报告题目: Linear Stability of Lagrange Homographic Orbits in the Planar Three-body Problem
报 告 人: 孙善忠 教授,首都师范大学数学科学学院
时间地点: 2012年7月19日下午2:00 思源楼S1013
摘       要: The linear stability of the Lagrangian homographic orbits in the planar three-body problem depends on the ecentricity and the mass parameter. We study this problem by Maslov-type index theory of Hamiltonian systems and perturbation theory of linear operators. The talk is based on the joint work with Xijun Hu and Yiming Long.
报告题目: Some Analytic Aspects of Conformally Invariant Fully Nonlinear Equations
报 告 人: Prof. Yanyan Li,Rutgers University,USA
时间地点: 2012年7月19日上午10:30 思源楼S712
摘       要: We will discuss some work on conformally invariant elliptic and degenerate elliptic equations arising from conformal geometry. These include results on Liouville type theorems, Harnack inequalities, and Bocher type theorems.
报告题目: The Glassey conjecture with radially symmetric data
报 告 人: Prof. Chengbo Wang,Zhejiang University
时间地点: 2012年7月11日下午4:00 思源楼S712
摘       要: In this talk, we will discuss the Glassey conjecture, which states that, for the nonlinear wave equations of the form $\Box u=|\nabla u|^p$, the critical exponent to admit global small solutions is given by $p_c=1+\frac{2}{n-1}$.
In a recent work with Kunio Hidano and Kazuyoshi Yokoyama, we verified the Glassey conjecture in the radial case for all spatial dimensions. Moreover, we are able to prove the existence with low regularity and sharp lifespan. The main idea is to exploit the KSS type estimates and the trace estimates.
When the spatial dimension is two, we need also to exploit the generalized Strichartz estimates, which was developed in our recent work with Chris Sogge and Hart Smith.
报告题目: Positive Solutions of Nonlinear Systems of elliptic type
报 告 人: Prof. Haiyan Wang,Arizona State Univ, USA
时间地点: 2012年7月9日上午10:30 思源楼S712
摘       要:  
报告题目: Compressible Navier-Stokes equations with temperature dependent dissipation
报 告 人: Prof. Ronghua Pan,Georgia Institute of Technology
时间地点: 2012年7月4日下午4:00 思源楼S1013
摘       要: From its physical origin, the viscosity and heat conductivity in compressible fluids depend on absolute temperature through power laws. The mathematical theory on the well-posedness and regularity on this setting is widely open. I will report some recent progress made on this direction, with emphasis on the lower bound of temperature, and global existence of solutions in one or multiple dimensions. This talk is based on joint works with Weizhe Zhang.
报告题目: On the Cauchy problem of 2D Euler-Poisson system
报 告 人: Prof. Dong Li,University of British Columbia
时间地点: 2012年6月21日下午2:00 思源楼S1013
摘       要:  
报告题目: Decomposision methods for interior inverse scattering problems
报 告 人: Prof. Sun Jiguang,Dept of Math., Delaware State University, USA
时间地点: 2012年6月18日下午3:30 思源楼S1013
摘       要:  
报告题目: Critical Thresholds in Restricted Euler-Poisson equations
报 告 人: Prof. Hailiang Liu,Iowa State University
时间地点: 2012年6月7日下午4:00 思源楼S712
摘       要: A fundamental physical model in many applications involves a moment equation for the velocity field. An important phenomenon exhibited by these models is the loss or persistence of $C^1$ regularity when initial velocity gradient crosses a critical threshold. In this talk we provide a description of the critical threshold phenomenon in multi-dimensional restricted Euler-Poisson (REP) equations. For three dimensional REP equations, we identified both upper-thresholds for finite time blow up of solutions and sub-thresholds for global existence of solutions, with thresholds depending on the relative size of the initial density and the eigenvalues of the initial velocity gradient matrix. These one-sided threshold conditions of initial configurations, corresponding to several situations of physical interest, are optimal. For attractive forcing case, these results also hold for arbitrary n-dimensions (n> 3).
报告题目: Existence and Multiplicty Results on Elliptic Systems of Lane-Emden Type in Unbounded omains
报 告 人: Dr. Sara Barile,University of Bari, Italy
时间地点: 2012年5月27日下午4:00 思源楼S703
摘       要:  
报告题目: Some problems with compressible Navier-Stokes systems
报 告 人: Prof. Zhouping Xin,Institute of Mathematical Sciences, Chinese University of Hong Kong
时间地点: 2012年4月1日上午10:00 思源楼S703
摘       要:  
报告题目: Bubbling Solutions for the Chern-Simons Model on a Torus
报 告 人: Prof. Shusen Yan,University of New England Australia
时间地点: 2012年1月10日上午10:00 思源楼S1013
摘       要: In this talk, I will present some recent results on the existence of bubbling solutions for a Chern--Simons model on a torus. This is a joint work with C.S. Lin in Taiwan University.
报告题目: Some Properties of Vector Fields on the Surfaces and its Application to the Stokes and Navier-Stokes Problems with Mixed Boundary Conditions
报 告 人: Prof. Tujin Kim,Institute of Mathematics Academy of Sciences DPR Korea
时间地点: 2011年12月15日下午2:30 思源楼S703
摘       要: On the parts of boundary where flow is orthogonal or tangent to the boundary some relations among strain, rotation, normal derivative and form of boundary surface are obtained.Relying on the relations, are given the variational formulations of the Stokes and Navier-Stokes problems with mixture of 7 kinds of boundary conditions involving velocity, pressure, rotation, stress and normal derivative conditions. Also, existence and uniqueness of solutions to the problems are considered.
报告题目: 高维守恒律方程的几个问题
报 告 人: 杨小舟 研究员,中科院武汉物理与数学研究所
时间地点: 2011年11月23日上午10:30 思源楼1013
摘       要:  
报告题目: Sharp geometric inequalities and applications to PDEs
报 告 人: 陆国震 教授,美国韦恩州立大学教授, 北京师范大学讲座教授
时间地点: 2011年11月22日下午4:00 思源楼712
摘       要: Geometric inequalitie s are important in analysis, geometry and PDEs. In this talk, we will review sharp geometric inequalities such as Sobolev and Poincare inequalities, Moser-Trudinger inequalities, Hardy-Littlewood-Sobolev inequalities and their applications to PDEs. We will also describe some recent results of such inequalities in the Heisenberg group and their applications to subelliptic PDEs.
报告题目: Block boundary value methods for delay integro-differentialequations
报 告 人: 张诚坚 教授,华中科技大学
时间地点: 2011年11月11日上午10:30 思源楼1013
摘       要:  
报告题目: 延迟模型的数值计算
报 告 人: 张诚坚 教授,华中科技大学
时间地点: 2011年11月4日上午10:30 思源楼1013
摘       要:  
报告题目: Maxwell方程与变分方法
报 告 人: 周焕松研究员,武汉物理与数学所
时间地点: 2011年10月22日上午9:00 思源楼1013
摘       要:  
报告题目: Global attractors for autonomous nonlinear evolutionary equations
报 告 人: 秦玉明 教授, 东华大学
时间地点: 2011年10月20日下午4:00 思源楼1013
摘       要: In this talk, we shall survey the existence theory of global attractors for autonomous nonlinear evolutionary equations and various methods in terms of compactness and continuity of asscoiated semigroups are aslo introduced.
报告题目: The Cauchy problem for a complex-valued heat equation with a quadratic nonlinearity
报 告 人: Professor Jong-Shenq Guo,Department of Mathematics, Tamkang University, Taiwan
时间地点: 2011年10月17日上午10:30 思源楼1013
摘       要: We study the Cauchy problem for a system of parabolic equations which is derived from a complex-valued equation with a quadratic nonlinearity. First we show that if the convex hull of the image of initial data does not intersect the positive real axis, then the solution exists globally in time and converges to the trivial steady state. Next, on the one dimensional space, we provide some solutions with nontrivial imaginary part that blow up simultaneously. Finally, we consider the case of asymptotically constant initial data and show that, depending on the limit, the solution blows up non-simultaneously at space infinity or exists globally in time and converges to the trivial steady state.
报告题目: Transonic Shocks for the compressible Euler Equations coupled with the Electric Fields
报 告 人: Prof. Tao Luo,Math. Sci. Center & Dept, Tsinghua Univ. , Morningside center of Math. CAS
时间地点: 2011年9月28日下午4:00 思源楼1013
摘       要: In this talk, I will present some results on the existence and non-existence of the unique and multiple solutions for the transonic shock problem for the compressible Euler equations coupled with the electric fields, and I will also discuss the results of their dynamical stability. This talk is based on the joint work with J. Rauch, C. Xie and Z. Xin.
报告题目: Multibump solutions of nonlinear Schrodinger equations with steep potential well and efinite potential
报 告 人: 唐仲伟 副教授,北京师范大学数学科学学院
时间地点: 2011年9月16日下午4:00 思源楼1013
摘       要: We are concerned with the existence of single- and multi-bump solutions of the equation $-\Delta u+(\lambda a(x)+a_0(x))u=|u|^{p-2}u$,\ \ $x\in{\mathbb R}^N$;here $p>2$, and $p<\frac{2N}{N-2}$ if $N\geg 3$. We require that $a\geg 0$ is in $L^\infty_{loc}({\mathbb R}^N)$ and has a bounded potential well $\Omega$, i.e.\ $a(x)=0$ for $x\in\Omegta$ and $a(x)>0$ for $x\in{\mathbb R}^N\setminus\bar {\Omega}$.Unlike most other papers on this problem we allow that $a_0\in L^\infty({\mathbb R}^N)$ changes sign. Using variational methods we prove the existence of multibump solutions $u_\lambda$ which localize, as $\lambda\to \infty$,near prescribed isolated open subsets $\Omega_1,\dots,\Omega_k\subset \Omega$. The operator $L_0:=-\Delta+a_0$ may have negative eigenvalues in $\Omega_j$, each bump of $u_\lambda$ may be sign-changing.
报告题目: Models for Solid-Solid Phase Transitions Driven by Configurational Forces
报 告 人: Prof. Peicheng Zhu, Basque Center for Applied Mathematics, Spain
时间地点: 2011年9月15日下午4:00 思源楼703
摘       要: Materials science has emerged as one of the central pillars of the modern physical
sciences and engineering. A central tenet of it is that many properties of a material are dominated by microstructures of the material. Therefore it is extremely important to study the formation and evolution of microstructure. Some microstructure is formed by phase transitions.We are intersted in phase transitions driven by configurational forces, in elastically deformablesolids (e.g. Steel, Shape memory alloy). To model this kind of phase transitions, a phase-field approach is used. We also discuss mathematical restults of the new models.
报告题目: On the nonlinear Klein-Gordon Systems in the presence of mass resonance
报 告 人: Prof. Hideaki Sunagawa, Osaka University, Japan
时间地点: 2011年9月8日下午4:00 思源楼703
摘       要:  
报告题目: Protein Sequence Analyses for Epitope Prediction
报 告 人: Dr. Hao-Teng Chang, Graduate Institute of Molecular System Biomedicine, China Medical University, Taiwan
时间地点: 2011年8月5日上午10:00 思源楼1013
摘       要: Bioinformatics tools for epitope prediction assist biologists to analyze the protein sequences/structures and design peptides for antibody generation and detection of the pathogen-infected antisera. Our group has studied the functional peptides for many years. Several methodologies were developed focusing on the prediction of antigenic regions and unique peptide antigens. Linear Epitope Prediction (LEP) tool was developed for calculating the sequence antigenicity score according to the physico-chemical propensities of each amino acid. Each physico-chemical propensity score is further modified by mathematical morphology methodology. LEP is advantage to extract local peaks within the relatively low antigenicity regions, and some of them are demonstrated as real epitopes by molecular biology experiments. Except LEP, we just reported LEPS which combined physico-chemical propensities with amino acid segmental features using SVM method. LEPS enhanced large number of specificity and positive prediction value. The overall accuracy was also increased. As we know, the antibody/antigen recognition always faces the problems of binding nonspecifically. A specific antigenic peptide is crucial for generating a specific antibody. In order to pick up the unique and antigenic peptides, Reinforced Merging Unique Segment (ReMUS), an advanced version of Reinforced Merging Algorithms (RMA), was developed to analyze sequence set with high similarity, and extract the unique regions within each individual protein sequence. In the ReMUS system, the unique regions, named unique peptide motifs (UPMs), were ranked according to the antigenicity and we found that UPMs involved in molecular interaction behaviors such as antigen-antibody, protein-DNA, and ligand-receptor interactions. Our three methodologies assist molecular biologists to analyze their sequences and provide prediction for designing biological experiments.
报告题目: On the Vlasov-Landau-Poisson system
报 告 人: Prof. Yan Guo,Brown University, USA
时间地点: 2011年8月2日下午4:00 思源楼703
摘       要: The classical Vlasov-Landau-Poisson system describes a plasma interacting with its own electrostatic force as well as grazing Coulombic collisions among charged particles. We will discuss recent construction of global in time solution to such a system.
报告题目: A Topological degree counting for some Liouville systems of mean field equations
报 告 人: Prof. Lei Zhang,University of Florida, USA
时间地点: 2011年7月29日下午4:00 思源楼1013
摘       要:  
报告题目: The Poincare inequality is an open ended condition
报 告 人: Prof. Xiao Zhong,University of Jyvaskyla,Finland
时间地点: 2011年7月29日下午3:00 思源楼1013
摘       要:  
报告题目: A New GL Anisotropic and Isotropic Invisible Cloak Without Exceeding Light Speed Violation
报 告 人: Professor Xie Ganquan,GL Lab, USA
时间地点: 2011年7月28日下午4:00 思源楼1013
摘       要: In this paper, we propose a new GL EM anisotropic and isotropic invisible cloak class without exceeding light speed. The GL cloak material in this paper is different from our paper ArXiv 1050.3999. The radial dielectric and permeanbility of GL EM cloak in this paper are large than one. The refractive index of the GL cloak material, n(r), is large than one or equal to one. A unconventional GL radial EM cloak modeling and inversion are proposed here. By searching in a distinctive class of the rational function of (h), h = r ? R1, the GL EM cloak modeling and inversion create GL EM invisible cloak class without exceeding light speed. The GL EM cloaks can be practicable by using conventional optical materials. he properties of our GL EM cloak and their proofs are presented in this paper. The novel EM wave propagation and front branching in the GL cloak by GL EM modeling are presented in this paper. The EM wave front propagation in GL cloak is behind of the front in free space. At time steps 118dt, in the GL cloak, the wave front is curved as a crescent like and propagates slower than the light in free space. At the time step 120dt, the EM wave inside of the GL EM cloak propagates slower than light speed, moreover, its two crescent front peaks intersect at a front branching point. At the front branching point, the front is split to two fronts. The novel front branching and crescent like wave propagation are displayed in figures in this paper. A more exciting breakthrough progress is that we discovered a isotropic EM invisible cloak without exceeding light speed violation.The isotropic dielectric and permeability cloaking material are proposed as (4-5) and (7) in this paper. All copyright and patent of the GL EM cloaks and GL modeling and inversion methods are reserved by authors in GL Geophysical Laboratory.
报告题目: Estimates for a parabolic system from composite material
报 告 人: Professor Li Yanyan,Rutgers University,USA
时间地点: 2011年7月21日下午4:00 思源楼1013
摘       要:  
报告题目: DISCONTINUOUS GALERKIN METHODS FOR MAXWELL'S EQUATIONS
报 告 人: 谢资清 教授, 湖南师范大学
时间地点: 2011年7月20日下午4:00 思源楼1013
摘       要:  
报告题目: Bose-Einstein Condensation and the Kompaneets Equation
报 告 人: Prof. Hailiang Liu,Iowa State University,USA
时间地点: 2011年7月13日下午4:00 思源楼1013
摘       要: A Bose-Einstein condensate (BEC) is the remarkable state of matter that spontaneously emerges when a system of bosons becomes cold enough. BEC for photons has been thought impossible until its recent experimental discovery by Martin Weitz and colleagues in Bonn. The simplest model for such a photon diffusion process is the Kompaneets equation. In this talk we focus on a model for the Kompaneets equation posed on a bounded interval subject to zero flux at finite energy. We shall discuss the global well-posedness for this model problem. Bose-Einstein condensation is shown to form in finite time when initial photon number is above a threshold. Below this threshold a condensate will develop for some initial data, but not for others. This talk is based on a joint collaboration with D. Levermore (UMD) and R. Pego (CMU)..
报告题目: Zero dissipation limit of 1d compressible Navier-Stokes equations
报 告 人: 张映辉 副教授,湖南理工学院
时间地点: 2011年7月12日上午10:00 思源楼1013
摘       要:  
报告题目: Some elliptic Problems
报 告 人: Prof. Li Congming,University of Colorado,USA
时间地点: 2011年7月9日上午10:00 思源楼1013
摘       要:  
报告题目: Weak Solutions to Cometary Flow Equations
报 告 人: Prof. Xianwen Zhang,Huazhong University of Science and Technology, Wuhan, China
时间地点: 2011年7月7日下午5:00 思源楼1013
摘       要: We discuss some nonlinear kinetic equations arising from the theory of astrophysical plasmas, existence of global weak solutions both for given external force fields and self-consistent Lorentz fields are established under physically reasonable conditions. Those results were achieved mainly based on asymptotic methods, especially on renormalization method and vanishing viscosity method.
报告题目: Global strong solution to N-S system with temperature-dependent heat conductivity in 1D
报 告 人: Prof. Ronghua Pan,Georgia Institute of Technology USA
时间地点: 2011年7月7日下午4:00 思源楼1013
摘       要: In common setting, viscosity and heat conductivity are chosen as constants in compressible N-S system. However, the Chapman-Enskog theory strongly suggests that both viscosity and head conductivity are propotional to non-negative power of absolute temperature, which introduces some critical difficulties in the analysis of this physical system. Some basic questions such as well-posedness are widely open for this case. As a very first step, we will Showhow to obtain a solid global theory when viscosity is constant but heat conductivity is a power of temperature. This talk based on a joint work with Weizhe Zhang.
报告题目: The Cucker-Smale flocking model interacting with an incompressible viscous fluid
报 告 人: Prof. Hyeong-Ohk Bae, Ajou University, Korea
时间地点: 2011年7月7日下午3:00 思源楼1013
摘       要:  
报告题目: Mathematical Theories on the Boltzmann Equation without Angular Cutoff
报 告 人: Prof. Tong Yang,City University of Hong Kong, China
时间地点: 2011年6月20日上午10:00 思源楼1013
摘       要: In this talk, we will present our series works on the Boltzmann equation without Angular cutoff. It is known that the singularity in the non-cutoff cross-section of the Boltzmann equation leads to the gain of regularity and gain of weight in the velocity variable. By defining and analyzing a non-isotropy norm which precisely captures the dissipation in the linearized collision operator, a new and precise coercivity estimate for the non-Cutoff Boltzmann equation for general physical cross sections can be given. Based on this, we succeed in establishing the well-posedness theory together with some qualitative study, such as regularity, non-negativity and convergence rate to the equilibrium for the Boltzmann equation without angular cutoff. This is about the joint works with R. Alexandre, Y. Morimoto, S. Ukai and C.-J. Xu.
报告题目: On the Question of Global Regularity for Three-dimensional Navier-Stokes Equations and Relevant Geophysical Models
报 告 人: Prof. Edriss S. Titi,Weizmann Institute, Israel and University of California,USA
时间地点: 2011年6月9日下午4:00 思源楼1013
摘       要: The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, the so-called the ``Primitive Equations'', is often prohibitively expensive computationally, and hard to study analytically. In this talk I will survey the main obstacles in proving the global regularity for the three-dimensional Navier-Stokes equations and their Geophysical counterparts.Even though the Primitive Equations look as if they are more difficult To study analytically than The three-dimensional Navier-Stokes equations I will show In this talk that they have a unique global(in time) regular solution for all initial data. Inspired by this work I will also provide a new Global regularity criterion for the three-dimensional Navier-Stokes equations involving the pressure. This is a joint work with Chongsheng Cao.
报告题目: Estimation of Dirichlet and Transmission Eigenvalues from near field Cauchy data
报 告 人: Professor Sun Jiguang Dept of Math, Delaware State University, USA
时间地点: 2011年6月8日下午4:00 思源楼703
摘       要: The Dirichlet and the transmission eigenvalue problems play an important role And have received a lot of attention in inverse scattering theory.This is due to the fact that Dirichlet and transmission eigenvalues can be determined from the far field data of the scattered wave and used to obtain estimates for the material properties of the scattering object. In this talk, we show that Transmission eigenvalues can be obtained from the near field Cauchy data.In particular, we Use the gap reciprocity method to estimate the lowest Transmission eigenvalue. Similar method can also be used to determine the Dirichlet eigenvalues.
报告题目: Recent progress on the surface quasi-geostrophic and related equations
报 告 人: Prof. Jiahong Wu, Oklahoma State University,USA
时间地点: 2011年5月30日下午4:00 思源楼712
摘       要: Fundamental issues such as the global regularity problem concerning the surface quasi-geostrophic (SQG) and related equations have attracted a lot of attention recently. Signi cant progress has been made on various fronts. This talk focuses on very recent advances on the generalized SQG equations, although some previous work on the SQG equation will also be summarized. We remark that these generalized equations are active scalar equations with the velocity fi elds determined by the Scalars Through general Fourier multiplier operators. The SQG equation is a special case of these general models and it corresponds to the Riesz transform. The results we will present for the generalized SQG equations are from three recent papers in Collaboration with D. Chae, P. Constantin, D. Cordoba and F. Gancedo.
报告题目: On some new fixed point algorithms for solving a curvature regularization induced 4th order PDE
报 告 人: Prof. Ke Chen, 英国Liverpool大学数学系
时间地点: 2011年5月17日下午4:00 思源楼712
摘       要:  
报告题目: Some mixed type problems in gas dynamics and geometry
报 告 人: Prof. Dehua Wang,University of Pittsburgh USA
时间地点: 2011年5月13日下午3:30 思源楼1013
摘       要: Some mixed elliptic-hyperbolic problems arising in gas dynamics and Differential geometry will be considered. In particular, the mixed type problems of the transonic flow past an obstacle and the isometric embedding will be discussed.Our recent results including the connection of the two problems will be presented.
报告题目: Review For The Stability For The Incompressible Flow On Exterior Domains
报 告 人: Prof. Hyeong-Ohk Bae,Ajou University, Korea
时间地点: 2011年2月22日下午3:00 晨兴605
摘       要: We review some results on the stability of the incompressible fluids in an exterior domain. We categorize the survey according to the values of the steady solutions and to the values of the far field velocity, and to the spatial dimension.
报告题目: Mathematics of flocking and Synchronization
报 告 人: Prof. Seung-Yeal Ha,Seoul National University Korea
时间地点: 2010年2月22日上午9:00 晨兴605
摘       要: Collective motions in the system of self-propelled particles like flocking and synchronization are ubiqutous in our daily life, and these emergent phenomena are group dynamics, which is different from the individual motion of particles.
In this talk, I will review the recent progress on the modeling of flocking and synchronization in terms of ODE and PDE. I will also discuss some mathematical works and questions needed for solutions in future.
报告题目: Bubbling solutions for a Chern-Simon model in a torus
报 告 人: Prof. Shusen Yan,University of New England Australia
时间地点: 2010年12月19日下午4:00 思源楼1013
摘       要:  
报告题目: The singular solutions and Global dynamics of diffusion equations with absorption
报 告 人: Prof. Qi Yuanwei,Univ. of Central Florida,USA
时间地点: 2010年12月16日下午4:00 思源楼703
摘       要:  
报告题目: Travelling Wavefronts of a Degenerate and Singular Parabolic Equation in Non-Divergence Form
报 告 人: 尹景学 教授, 华南师范大学(国家杰出青年基金获得者)
时间地点: 2010年11月11日下午4:00 思源楼712
摘       要:  
报告题目: Conformally invariant nonlinear Equations and isolated singularities
报 告 人: Prof. Yanyan Li, Rutgers University,USA
时间地点: 2010年8月10日下午4:00 思源楼1013
摘       要:  
报告题目: Quasilinear elliptic equations in Heisenberg group
报 告 人: Prof. Zhong Xiao, University of Jyvaskyla, FINLAND
时间地点: 2010年7月30日下午4:00 思源楼703
摘       要:  
报告题目: Some Robust Variants of Linear Sampling Methods for Inverse Obstacle Scattering
报 告 人: Prof. Jun Zou,Dept. of Math., Chinese University of Hong Kong
时间地点: 2010年7月15日下午3:00 思源楼1013
摘       要:  
报告题目: Radiation conditions for wave in essentially stratified midium
报 告 人: Prof. Yongzhi Steve Xu,Dept. of Math.,Univ. of Louisville, USA
时间地点: 2010年7月15日下午4:00 思源楼1013
摘       要: Waves from a point source in a homogeneous medium will propagate spherically. This can be described by the Sommerfeld radiation condition. However, it is hard to usesimple formula to describe radiation conditions for wave propagation in a stratified medium. A generalized Sommerfeld radiation was proposed by Xu in 1990, applying contour integral and asymptotic approximation. The study in this area becomes more active recently. Papers in 2009 and 2010 from different aspects presented regorous analysis for results similar to Xu's condition.On the other hand, Chandler-Wilde, Zhang and their coworkers introduced the upward propagating radiation condition for wave in essentially homogeneous Medium with rough boundary. This talk will discuss the radiation conditions, and introduce an upward propagatingradiation condition and a sideward radiation condition for waves in essentially layered medium with bounded or unbounded perturbation and rough surface.Some related direct and inverse scattering problems will be discussed.
报告题目: Fully Nonlinear Second-Order PDEs and Their Numerical Solutions
报 告 人: Prof. Xiaobing Feng,Professor in Dept of Mathematics,The University of Tennessee, USA
时间地点: 2010年7月6日下午4:00 思源楼712
摘       要:  
报告题目: Numerical Methods and Computation of Aerosol Distribution Prediction in Atmospheric Environment
报 告 人: Prof. Dong Liang, Dept. of Math.and Statistics York University, Canada
时间地点: 2010年7月5日下午3:00 思源楼1013
摘       要: Abstract: Aerosol science is a subject of growing importance due to its effect on global environment. Aerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. The general aerosol dynamic equations are the nonlinear integro-differential equations on time, particle size and space, which describe Different processes of atmospheric aerosols including condensation, nucleation, coagulation, deposition, sources as well as turbulent mixing. It is an important and challenging task to develop efficient numerical methods to solve the general aerosol dynamic equations.In this talk, I will introduce our recent research results in this field, including second order characteristics method and adaptive characteristics wavelet algorithm for aerosol dynamic equation, moving cut HDMR approach for aerosol thermodynamic equilibrium equations, and splitting adaptive characteristics wavelet algorithm for general spatial aerosol dynamics. Numerical experiments are given to show the efficiency of our approaches.
报告题目: Infinitely many positive solutions for elliptic problems with critical or super critical exponents
报 告 人: Prof. Shusen Yan, University of New England Australia
时间地点: 2010年7月5日下午4:00 思源楼1013
摘       要: We discuss elliptic problems involving critical or super critical Sobolev exponents. We will find conditions on the domain such that these problems have infinietly many positive solutions.
报告题目: The Heat Convection and Navier-Stokes Equations in Time-Dependent Domain with Velocity-Pressure Boundary Conditions
报 告 人: Prof.Tujin Kim, Institute of Mathematics, Academy of Sciences, DPR Korea
时间地点: 2010年7月1日下午4:00 思源楼1013
摘       要:  
报告题目: Non-homogeneous system of isentropic gas dynamics
报 告 人: Prof. Lu Yunguang(陆云光)哥伦比亚科学院院士,National University of Colombia COLOMBIA
时间地点: 2010年7月1日下午3:00 思源楼1013
摘       要:  
报告题目: 不可压Navier-Stokes方程的一些研究进展
报 告 人: 周勇教授, 浙江师范大学
时间地点: 2010年6月28日上午10:30 思源楼712
摘       要:  
报告题目: Partial regularity of non-Newtonian incompressible Navier-Stokes equations for shear thickening fluids
报 告 人: Prof. Hyeong-Ohk, Bae University, Republic of Korea
时间地点: 2010年6月28日上午9:30 思源楼1013
摘       要:  
报告题目: Liouville Type Theorems and the Classification of Solutions to the HLS systems
报 告 人: Prof. Congming Li, Univ. of Colorado at Boulder USA
时间地点: 2010年6月25日下午4:00 思源楼712
摘       要: The main object is the study of nonnegative solutions to the integral system derived from the well known Hardy-Littlewood-Sobolev inequality in both weighted and non-weighted form. We begin with a short/incomplete review of the related results and problems. The main Focus is on the classification of solutions in the `critical-case' and on the Liouville type theorems in the `subcritical case'. The well-known Land-Emden conjecture is a Liouville type `theorem' in a special case of the `subcritical' type HLS systems.We then present some integral type estimates -- a key ingredient in deriving both classification and the Liouville type theorem.As an application, we use the special integral type estimates to derive the asymptotic expansion of the solutions at infinity as well as at the possible interior singular point.
报告题目: Sharp boundary condition and Well-posedness of the FENE Dumbbell model for polymeric flows

报 告 人: Prof. Hailiang Liu, Iowa State University, USA
时间地点: 2010年6月21日下午4:00 思源楼1013
摘       要: In this talk I shall focus on the well-posedness for the FENE Dumbbell model for polymers under some sharp boundary requirement. The wellposedness of the FENE model that consists of The incompressible Navier-Stokes equation and the Fokker-Planck equation has been studied intensively in literature, mostly with the zero flux boundary condition. Here we identify least boundary requirements for different ranges of Dumbbell extension parameter. The distribution near boundary needs to approach zero faster than the distance function or its variation. Moreover, such boundary requirement still ensures that the distribution is a probability density. The sharpness of such boundary requirement is shown by construction of infinitely many solutions when the distribution approaches zero slower than the critical rate.
报告题目: Relaxation Methods for Image Denoising Difference Scheme
报 告 人: Prof. Rong-Qing Jia, University of Alberta,Canada
时间地点: 2010年6月10日上午10:00 思源楼712
摘       要:  
报告题目: Entropy Dissipation and Hyperbolic Balance Laws
报 告 人: Prof. Ronghua Pan, School of Mathematics, Georgia Institute of Technology, USA
时间地点: 2010年6月3日上午10:00 思源楼1013
摘       要: Entropy dissipation principle plays important roles in the theory of hyperbolic Balance laws, ranging from local existence of classical solutions, stability of shock waves, invariant region theory,to the large time behavior of weak solutions. Recent developments focus on the application to the large time asymptotic behavior of large weak solutions in compressible Euler equations with damping, Euler-Poisson equations for semi-conductor devices, and relaxation system.The talk will emphasize the recent results on the global stability of large solution to the compressible Euler equations With relaxation, based on the join work with Q. Ju and Y. Li.
报告题目: Well-posedness of a class of non-Newtonian fluids
报 告 人: 许孝精 副教授,北京师范大学
时间地点: 2010年6月3日下午4:00 思源楼1013
摘       要:  
报告题目: Mathematical Modeling, Analysis and Simulations of Chemotaxis
报 告 人: Prof. Zhi-An Wang, Department of Mathematics Vanderbilt University
时间地点: 2010年6月3日下午3:00 思源楼1013
摘       要:  
报告题目: Characterization of objects in periodic structures
报 告 人: Prof. Jiguang Sun, Delaware State University, USA
时间地点: 2010年5月26日下午4:00 思源楼1013
摘       要:  
报告题目: Some results on fractional differential equations
报 告 人: 韦忠礼 教授,山东大学
时间地点: 2010年5月24日上午9:30-10:30 思源楼1013
摘       要: The report is divided into four parts. In first part, we introduce some definitions of fractional integrals and derivative, and discuss the properties of the well-known Mittag--Leffler function. In second part, we consider the existence and uniqueness of solution of the initial value problem for fractional differential equation involving Riemann--Liouville sequential fractional derivative by using monotone iterative method. In third part, we consider the existence of solution of the periodic boundary value problem for fractional differential equation involving Riemann-Liouville sequential fractional derivative by means of the method of Upper And lower solutions and Schauder fixed point theorem. In last part, we investigate the existence of positive solutions of singular superlinear (or sublinear) boundary value problems for fractional differential equation involving Caputo fractional derivative, a necessary and sufficient condition for the existence of $C^3[0,1]$ positive solutions is given by means of the fixed point theorems on cones.
报告题目: Global solutions for the multi-dimensional magnetohydrodynamics
报 告 人: Prof. Dehua Wang, University of Pittsburgh,USA
时间地点: 2010年5月20日下午4:00 思源楼712
摘       要: Various global solutions for the multi-dimensional magnetohydrodynamics will be considered. In particular, the topics that will be discussed include global weak solutions in the compressible case, the incompressible limits from the vanishing Mach numbers and from the hydrodynamic limit of the Vlasov-Maxwell-Boltzmann equations, and the global well-posedness in Besov spaces for the incompressible case with zero magnetic diffusivity.
报告题目: Image segmentation
报 告 人: Prof. Dadong Wang, 澳大利亚联邦科学与工业研究组织
时间地点: 2010年4月29日下午4:00-5:00 思源楼712
摘       要: .
报告题目: Prof. Hyeong-Ohk Bae
报 告 人: Prof. Hyeong-Ohk Bae (Ajou University, Korea )
时间地点: 2010年2月4日下午4:00-5:00 思源楼703
摘       要: The existence of global regular solutions to the equations describing compressible Barotropic viscous motions which are close to some special sufficiently regular solutions is proved. The necessary estimate is proved by the energy method Appropriate for the compressible Navier-Stokes equations. Finally, the existence is proved by the method of successive approximations. We have to underline that the solutions is not small because we have a smallness condition on the difference between our solutions and some special sufficiently regular solution. By the special solution we mean a sufficiently regular solution to the compressible Navier-Stokes Equations with some symmetry. The following examples of special solutions are known: spherically symmetric or axially symmetric.
报告题目: 拟线性椭圆型方程的大解
报 告 人: 王明新 教授 (哈尔滨工业大学,东南大学 )
时间地点: 2010年1月18日上午10:00-11:00 思源楼1013
摘       要: .
报告题目: Rigorous derivation of shallow water equations from Navier Stokes equations with a free surface
报 告 人: Prof. P.Noble (University of Lyon, France)
时间地点: 2010年1月18日下午4:00-4:00 思源楼1013
摘       要: Shallow water equations are widely used to model the motion of a relatively thin layer of fluid. They are usually derived heuristically from Navier Stokes equations with a Free surface (or a simplified version like hydrostatic NS or boundary layer equations) and as a result there is a lack of consistance. In this talk, I will present two formal derivations of shallow water model, associated to Dirichlet condition or Navier slip condition at the bottom.I will show how these formal computations are proved to be rigorous.The main ingredients are a Lagrangian formulation of the problem in the neighbourhood of an approximate solution of Navier Stokes equations, built with a solution of a shallow water system and appropriate Sobolev estimates in thin domains.
报告题目: Low mach number limit for non-isentropic compressible flow
报 告 人: Prof. Didier Bresch (University of Savoie, France)
时间地点: 2010年1月18日下午3:00-4:00 思源楼1013
摘       要:  
报告题目: A fully nonlinear version of the Yamabe problem on manifolds with boundary
报 告 人: Prof. Yanyan Li (Rutgers University, USA)
时间地点: 2010年1月13日下午4:00-4:00 思源楼1013
摘       要:  
报告题目: $L^1$-contraction in viscous scalar conservation laws: Unconditional stability
报 告 人: Prof. Denis Serre (Ecole Normale Supérieure de Lyon, France)
时间地点: 2010年1月12日下午4:00-4:00 思源楼1013
摘       要: In scalar conservation laws of various type (insviscid, viscous, ...), which are evolutionnary PDEs, the solution semi-group is a contraction in the $L^1$-distance.However, the contraction is not necessarily strict. We investigate whether simple patterns, as constant states or shock fronts, are asymptotically stable in this $L^1$-distance. The answer is surprisingly simple, but the proof is amazingly subtle.
报告题目: Infinitely Many Positive Solutions for Some Elliptic Problems
报 告 人: Prof. Shusen Yan (The University of New England Australia)
时间地点: 2010年1月7日下午4:00-4:00 思源楼712
摘       要:  
报告题目: On the rigidity of minimal mass solutions for focusing mass critical nonlinear Schrodinger equation
报 告 人: 张晓轶 副研究员 (中科院数学与系统科学院)
时间地点: 2010年1月7日下午3:00-4:00 思源楼712
摘       要:  
2009年
报告题目: Finding Multiple Solutions to Elliptic PDE In interior/Exterior Domains with Nonlinear Boundary Conditions
报 告 人: Prof. Zhou Jianxin (Texas A & M University,USA)
时间地点: 2009年12月16日下午10:00-11:00 思源楼703
摘       要:  
报告题目: A new variational model for Segmenting selective features of an image
报 告 人: Prof. Ke Chen (Centre for Mathematical Imaging Techniques, University of Liverpool, UK)
时间地点: 2009年11月18日下午4:00-5:00 思源楼1013
摘       要: Image segmentation refers to the automatic process of dividing an image into classes or categories, corresponding to different objects and the background of the image. Variational models achieve this by minimizing a suitable functional, often in the framework of D. Mumford and J. Shah(1989). Commonly studied models segment all features in an image, with the most well known work due to T. F Chan and L.Vese (2001). However practical Applications may demand methods to be able to select features e.g. isolating the liver in medical CT images. Recently, C. Gout, C. Le Guyader and L. Vese (2005,2008) proposed geodesic active contours methods for selective segmentation. As they use an edge detector, robustness can be an issue if noise is present. In this work, we propose a new modification of this model by utilizing region based segmentation ideas. Reliable results have been achieved. This is joint work with N. Badshah (Peshawa, Pakistan).
报告题目: Hunting Non-linear Mathematical Butterflies
报 告 人: Prof. Nalini Joshi (悉尼大学,澳大利亚科学院院士)
时间地点: 2009年11月13日下午4:00-5:00 思源楼703
摘       要: The utility of mathematical models relies on their ability to predict the future from a known set of initial states. But there are non-linear systems, like the weather, where future behaviours are unpredictable unless their initial state is known to infinite precision. This is the "butterfly effect". I will show how to analyse functions to overcome this problem for the classical Painlevé equations, differential equations that provide archetypical non-linear models of modern physics.
报告题目: On the singularity formation of a 3D model for Incompressible Euler and Navier-Stokes equations
报 告 人: Prof. Thomas Y. Hou (California Institute of Technology, USA)
时间地点: 2009年9月17日下午4:00-5:00 思源楼703
摘       要: We study the singularity formation of a recntly proposed 3D model for the incompressible Euler and Navier-Stokes equations. This 3D model is derived from the axisymmetric Navier-Stokes equations with swirl using a set of new variables. The model preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected. If we add the convection term back to our model, we would recover the full Navier-Stokes equations. We will present numerical evidence which supports that the 3D model may develop a potential finite time singularity.We will also analyze the mechanism that leads to these singular events in the new 3D model and how the convection term in the full Euler and Navier-Stokes equations destroys such a mechanism, thus preventing the singularity from forming in a finite time. Finally, we prove rigorously that the 3D model develops finite time singularities for a large class of initial data with finite energy and appropriate boundary conditions. This work may shed interesting light into the stabilizing effect of convection for 3D incompressible Euler and Navier-Stokes equations.
报告题目: 一类来自微机电系统模型的椭圆和抛物方程
报 告 人: Prof. Dong Ye (Laboratoire Mathematiques et Application de Metz Universite de Metz, France )
时间地点: 2009年8月31日下午4:00-5:00 思源楼1013
摘       要:
.
报告题目: GL Double Layer Cloak and Reciprocal Law
报 告 人: Prof. Jianhua Li (GL Geophysical Laboratory, USA)
时间地点: 2009年8月28日下午4:00-5:00 思源楼1013
摘       要:
.
报告题目: 3D GL Metre Carlo Inversion and Cloak
报 告 人: Prof. Ganquan Xie (GL Geophysical Laboratory, USA)
时间地点: 2009年8月28日下午3:00-4:00 思源楼1013
摘       要:
.
报告题目: Finite time blow up for Lagrangian mean curvature flow
报 告 人: Prof. Yuan Yu (University of Washington, USA)
时间地点: 2009年7月30日下午4:00-5:00 思源楼1013
摘       要:
.
报告题目: Global regularity of the 4d restricted euler equations
报 告 人: Prof. Hailiang Liu(Iowa State University, USA)
时间地点: 2009年7月30日下午3:00-4:00 思源楼1013
摘       要: In this talk I shall report recent progress on the study of critical threshold phenomena in time-dependent Eluerian PDEs, with a particular focus on the Restricted Euler (RE) equations. Using the spectral and trace dynamics we identify the critical thresholds for 3D and the 4D restricted Euler equations. It is well known that the 3D RE solutions blow up.Projected on the 3-sphere, the set of initial eigenvalues which give rise to bounded stable solutions is reduced to a single point, which confirms that 3D RE blowup is generic. In contrast, we identify a surprisingly rich set of the initial spectrum on the 4-sphere which yields global smooth solutions; thus, 4D regularity is generic.
报告题目: Stability in Stefan problem with surface tension
报 告 人: Prof. Yan Guo (Brown University, USA)
时间地点: 2009年7月23日下午4:40-5:40 思源楼712
摘       要:
We develop a high-order energy method to study the classical Stefan problem with surface tension effect. We prove that a flat surface is always nonlinearly stable. On the other hand, a steady circle can be either stable or unstable,depending on the its relative size.
报告题目: Isometric embedding of higher-dimensional Riemannian manifolds
报 告 人: Prof. Qing Han (University of Notre Dame and Peking University)
时间地点: 2009年7月23日下午3:30-4:30 思源楼712
摘       要:
In this talk, we will derive a differential system for the local isometric embedding of Riemannian manifolds in Euclidean space of the ideal dimension. We will solve
this system in dimension three under appropriate assumptions on Riemann curvature.
报告题目: The Navier-Stokes Equations
报 告 人: Prof. Werner Varnhorn (Kassel University, Germany)
时间地点: 2009年7月10日下午4:00-5:00 思源楼1013
摘       要:
More than 2500 years after the famous statement παντα ρει by Heracleitos the investigation of the mechanical and dynamical behavior of fluid flow is more than ever of fundamental importance. Due to a large number of technical, experimental and computational innovations And related theoretical problems the investigation of fluid flow represents a challenging and exciting subject requiring a wide variety of profound mathematical methods, efficient numerical algorithms and complex experimental simulations. Fascinating from the mathematical point of view, of course, is the fact that the fundamental equations of Navier-Stokes, formulated the first time by the French engineer Navier in 1822, could not be solved in the general three-dimensional case up to now. So the famous American Clay Mathematics Institute created the Navier-Stokes Millennium Price Problem and offered one Million US-Dollar for itssolution, stating: "Although the Navier-Stokes equations were written down in the 19thCentury, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory, which will unlock the secrets hidden in the Navier-Stokes equations".The lecture introduces the Navier-Stokes equations from an historical and physical point of view, touches some fundamental mathematical problems of viscous incompressible fluid flow and discusses currently still open questions .
报告题目: Bubbling Solutions for the Chern-Simons Model on a Torus
报 告 人: Prof. Yan Shusen(Univ.New England, Australia)
时间地点: 2009年7月7日下午4:00-5:00 思源楼1013
摘       要:
.
报告题目: 2D viscous Boussinesq system on a bounded domain
报 告 人: Prof. Ronghua Pan(Georgia Institute of Technology, USA)
时间地点: 2009年7月2日下午4:00-5:00 思源楼1013
摘       要: 2D viscous Boussinesq system not only models the geographic and oceanic flows for climate sciences, but also serves as an important approximate model to the 3D incompressible flows sharing the key vortex stretching effects. We will prove the global regularity for the system on a bounded domain with smooth boundary and non-slip boundary data. This is a joint work with M. Lai and K. Zhao.
.
报告题目: Diffusion waves and hyperbolic damped p-systems
报 告 人: Prof. Ming Mei(McGill University & Champlain College, Canada )
时间地点: 2009年7月2日下午3:00-4:00 思源楼1013
摘       要: For the 2x2 hyperbolic p-system with damping, its asymptotic profile has been traditionally regarded as the self-similar solution, the so-called Diffusion wave, to the corresponding parabolic equation by the Darcy's law, and the convergence of the original solution to the diffusion wave has been intensively studied by many people. However, by a deep observation and a heuristic analysis, we realize that the best asymptotic profile for the solution to the Cauchy problem of the $p$-system with damping is a particular solution to the corresponding nonlinear parabolic equation with a specified initial data, and we further obtain the optimal convergence rates to this particular asymptotic profile. These new rates are much better than the existing convergence rates to the diffusion waves. Our results essentially improve and develop the revious studies. Finally, some numerical simulations are carried out, which also confirm our theoretical results.
.
报告题目: Estimates for Equations with Foliations
报 告 人: Prof. Lihe Wang (The University of Iowa, USA )
时间地点: 2009年6月30日下午3:00-4:00 思源楼1013
摘       要:
.
报告题目: Critical Thresholds in a Quasi-linear Hyperbolic Model of Blood Flow
报 告 人: Prof. Tong Li (The University of Iowa, USA )
时间地点: 2009年6月30日下午2:00-3:00 思源楼1013
摘       要:
.
报告题目: Oscillations and Instabilities for Boundary Value Problems in Multi-dimensions
报 告 人: Prof.C. Jones (University of North Carolina, USA )
时间地点: 2009年6月25日下午4:00-5:00 思源楼1013
摘       要:
.
报告题目: Boltzmann- Vlasov Equation
报 告 人: Prof.Alexander Sinitsyn (Institute System Dynamics and Control Theory Irkutsk, Russia )
时间地点: 2009年6月19日上午10:30-11:30 晨兴中兴410
摘       要:
.
报告题目: A Complex Approach to Processing Spatially Distributed Data
报 告 人: Prof. Igor Bychkov (Director of Institute System Dynamics and Control Theory Irkutsk, Russia, SB of RAS, Corr. Member of RAS )
时间地点: 2009年6月19日上午9:30-10:30 晨兴中兴410
摘       要:
.
报告题目: Infinitely many solutions for elliptic problems with critical growth
报 告 人: Prof. Shusen Yan (University of New England, Australia)
时间地点: 2009年1月7日下午4:00-5:00 思源楼712
摘       要:
.
报告题目: Existence of solution to parabolic equation with mixed boundary condition on non-cylindrical domain
报 告 人: Prof. Tujin Kim (Institute of Mathematics, Academy of Sciences, DPR Korea)
时间地点: 2009年1月7日下午3:00-5:00 思源楼712
摘       要:
.
2008年
报告题目: The transonic shocks in nozzles
报 告 人: 尹会成 教授 (南京大学现代数学所常务副所长)
时间地点: 2008年11月19日下午4:00-5:00 思源楼712
摘       要: In the book "Supersonic flow and shock waves'' of Courant and Friedrichs, the following transonic shock phenomena in the de Laval nozzles are described: Given the appropriately large receiver pressure $p_r$, if the upstream flow is still supersonic behind the throat of the nozzle,then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes $p_r$. When the end pressure $p_r$ varies and lies in an appropriate scope, in general,it is expected that a curved transonic shock is still formed in a nozzle. In this talk, we solve this problem for the two-dimensional or three-dimensional steady Euler systems with the variable exit pressures in the large curved nozzles. This is a joint work with Prof.Xin Zhouping and Dr.Li Jun.
.
报告题目: Sharp functional estimate of Boltzmann operators
报 告 人: Prof. Chaojiang XU (Rouen University, France)
时间地点: 2008年10月30日下午4:00-5:00 思源楼703
摘       要: In this talk, we prove a sharp upper bounded estimate for Boltzmann operators without cutoff in Sobolev space and also a sharp coercivity estimates. The main
tools is microlocal analysis of nonlinear equations. We give also some application of those estimates.
报告题目: A general existence theorem for Hamilton-Jacobi equation and differential inclusions
报 告 人: Prof. B.Dacorogna (Ecole Polytechnique Federale de Lausanne (EPFL)SWITZERLAND )
时间地点: 2008年10月29日下午4:00-5:00 思源楼703
摘       要:  
报告题目: 附着在向量场(或自治系统)上无穷维Lie代数的模结构
报 告 人: 管克英 教授 (北京交通大学)
时间地点: 2008年9月11日下午4:00-5:00 思源楼1013
摘       要:  
报告题目: Gradient estimates for elliptic equations and systems from Composite material
报 告 人: Prof. Li Yanyan (Rutgers Univ., USA)
时间地点: 2008年9月4日下午4:00-5:00 思源楼1013
摘       要:  
报告题目: Heat Flows of Linear Growth Maps and Color Image Denoising
报 告 人: Prof. Xiaobing Feng (Department of Mathematics University of Tennessee USA)
时间地点: 2008年7月18日上午10:00-11:00 思源楼703
摘       要: In this talks I shall first present some recent developments on p-harmonic map heat flows, in particular, for the case p=1, and flows of linear growth maps into spheres. I shall then discuss applications of these geometric flows to color image denoising based on the chromaticity and brightness decomposition.Finally, I shall present some numerical methods and Computer simulations for the proposed color image denoising models. This is a joint work with John Barrett of Imperial College (UK), Andreas Prohl of University of Tuebengin(Germany), and Minun Yoon of University of Tennessee.
报告题目: Extensions of bifurcation from simple eigenvalue theorem
报 告 人: Prof. Junping Shi (College of William and Mary, Virginia, USA, and Harbin Normal University, Harbin, China)
时间地点: 2008年7月17日下午4:00-5:00 思源楼1013
摘       要: Nonlinear equations can often be formulated as a nonlinear operator equation in Banach spaces, and the linearized operators are often linear Fredholm operators of index zero. Examples include a large class of quasilinear elliptic systems with nonlinear boundary conditions. A classical theorem of Crandall And Rabinowitz states that a bifurcation occurs at a simple eigenvalue along a branch of trivial solutions, And near the bifurcation point, the solution set consists of a line segment and a curve crossing it. We show a bifurcation theorem generalizing the classical one without a priori knowledge of a line of trivial solutions, which can also be used in perturbation problem of degenerate solutions. In another extension we show that the bifurcation from a simple eigenvalue is indeed global, which is also an extension of Rabinowitz's global bifurcation theorem which requires compactness. The talk is based on joint work with Ping Liu, Yuwen Wang of Harbin Normal University, and Xuefeng Wang of Tulane University.
报告题目: Compressible Vortex Sheets and Free Boundary Problems
报 告 人: Prof. Gui-Qiang Chen (Northwestern University (USA) and Fudan University (PRC))
时间地点: 2008年7月17日上午10:00-11:00 思源楼703
摘       要: Compressible vortex sheets are fundamental waves, along with shock and rarefaction waves, in entropy solutions to multidimensional hyperbolic Systems of conservation laws.Understanding the behavior of compressible vortex sheets is an important step towards our full understanding of fluid motions and the behavior of entropy solutions.In this talk, we will show how the existence and stability of compressible vortex sheets can be Formulated as a free boundary problem and will discuss some recent developments in the study of such a problem for compressible vortex sheets in multidimensional gas dynamics and magnetohydrodynamics. Further remarks, trends, and open problems in this direction will also be addressed .
报告题目: Semi-classical dynamics in Schroedinger Equations: Convergence and Computation
报 告 人: Prof. Hailiang Liu (Iowa State University,USA)
时间地点: 2008年7月10日下午4:00-5:00 思源楼1013
摘       要: .
报告题目: Auto-Catalytic Chemical Reactions--Global Dynamics and Traveling Waves
报 告 人: Prof. Yuanwei Qi (University of Central Florida USA )
时间地点: 2008年7月10日下午3:00-4:00 思源楼1013
摘       要: .
报告题目: Existence and uniqueness of positive solutions for an integral boundary value problem
报 告 人: 杨志林 教授 (青岛理工大学)
时间地点: 2008年7月3日下午4:00-5:00 思源楼1013
摘       要: This paper deals with the existence and uniqueness of positive solutions for the second-order integral boundary value problem. The main tools used in the proofs are the a priori estimate method and the Leray-Schauder fixed point theorem .
报告题目: Some old and new results on liquid crystals
报 告 人: Prof. Min-Chun Hong (University Queensland, Australia)
时间地点: 2008年6月26日下午4:00-5:00 思源楼1013
摘       要: A liquid crystal is a mesomorphic phase of a material which occurs between its Liquid and solid phase. The material is composed of rod like molecules which display orientational order, unlike a liquid, but lacking the lattice structure of a solid. There are a lot of analytical and computational issues, which arises in the attempt to study static equilibrium configurations. Main purpose of this talk is to survey some old related results on relaxed energies for harmonic maps and liquid crystals. We also outline some new approach in the study of liquid crystals .
报告题目: On the Analysis of Landau-Lifshitz-Gilbert equation
报 告 人: Prof. Changyou Wang (Department of Mathematics, University of Kentucky )
时间地点: 2008年6月26日下午3:00-4:00 思源楼1013
摘       要: The Landau-Lifshitz-Gilbert equation describes the evolutional dynamics of magnetic moment fields of ferromagnetic material, first proposed by Landau-Lifshitz in 1935. It has been extensively studied by physics and material sciences. Yet there are still many analytic issues that remain to be understood from mathematical view of points. In particular, the problem of formation of singularity and refined regularity property have drawn considerable interests. In this talk, I will survey some recent works on the existence of finite time singularity and partially regular solutions to the Landau-Lifshitz-Gilbert equation in higher dimensions. It is based on two joint works with Ding, Shijin, and Ding, Shijin & Liu, Xiangao respectively .
报告题目: A Null-space free Jacobi-Davidson iteration for Maxwell's operator
报 告 人: Prof. Wei-Cheng Wang (Tsing-Hau University, Taiwan )
时间地点: 2008年6月12日下午4:00-5:00 思源楼1013
摘       要: We present an efficient null-space free method to compute the positive eigenvalues of the degenerate elliptic operator arising from Maxwell's equations. We focus on a class Of spatially compatible Discretizations such as Yee's scheme or co-volume discretization, Which guarantees the existence of a discrete vector potential. During the Jacobi-Davidson iteration, the correction process is applied to the vector potential instead. The correction equation only needs to be solved approximately as in the standard Jacobi-Davidson approach.The computational cost of the transformation from the vector potential to the correcting vector is negligible. As a consequence, the orrected subspace Automatically stays out of thenull-space and no extra projection step is needed. Numerical evidence confirms that the new method is much more efficient than the original Jacobi-Davidson method .
报告题目: Kinetic Theory and Gas Dynamics
报 告 人: Prof. Hyeong-Ohk Bae (Ajou University,亚洲大学,Korea )
时间地点: 2008年6月5日下午4:00-5:00 思源楼709
摘       要: By means of an inequality of Poincar\'e type, a weak Harnack inequality for the gradient of a solution and an integral inequality of Campanato type, it is shown that a
solution to certain degenerate parabolic system is locally H\"older continuous.The system is a generalization of $p$-Laplacian system.Using a difference quotient Method and Moser type iteration it is then proved that the gradient of a solution is locally bounded. Finally using the iteration and scaling it is shown that the gradient of the solution satisfies a Campanato type integral inequality and is locally H\"older continuous .
报告题目: Kinetic Theory and Gas Dynamics
报 告 人: Prof..Taiping Liu (Stanford University)
时间地点: 2008年5月27日下午4:00-5:00 思源楼712
摘       要: .
报告题目: Bound states for a nonlinear Schrodinger system
报 告 人: Dr. Zhi-Qiang Wang (Utah State University,USA)
时间地点: 2008年5月15日下午4:00-5:00
摘       要: .
报告题目: Stability of traveling waves for the 1D Gross-Pitaevskii equation
报 告 人: Prof. Zhifei Zhang(北京大学)
时间地点: 2008年5月7日下午4:00-5:00
摘       要: In this paper, we prove the nonlinear orbital stability of traveling waves with zero velocity for the one-dimensional Gross-Pitaevskii equation by using The inverse scattering method.
报告题目: Vanishing of Vacuum States and Blow-up of Global Weak Solutions of the Navier-Stokes Equation for Compressible Fluids
报 告 人: Prof. Hailiang Li(首都师范大学)
时间地点: 2008年5月7日(星期三)下午3:00-4:00
摘       要: The initial boundary value problem for the compressible Navier-Stokes equation with density-dependent viscosity is considered in the present talk on spatial bounded domain. The entropy weak solutions for general large initial data satisfying finite initial entropy are proven to exist globally in time, and any possible vacuum state is shown to vanish within finite time so long as it exists initially or within some finite time interval. The global entropy weak solution becomes a strong solution after the vanishing of vacuum states. Moreover, it is shown that if there exists vacuum state within some time interval (for short time, for instance) of the global entropy weak solution whose velocity derivative is bounded, the velocity blows up within finite time. The existence and uniqueness of such weak solution whose velocity has bounded spatial derivative are also proven for short time subject to more regular initial data with vacuum.
报告题目: A GL EM-Flow-Cold-Stress Coupled Modeling and Inversion For Icing Disaster On High Voltage Network
报 告 人: Prof. Xie Ganquan (GL Geophysical Laboratory USA)
时间地点: 2008年5月6日下午4:00-5:00
摘       要:  
报告题目: Periodic Travelling Waves in a Cylinder with Saw-toothed Boundary
报 告 人: 娄本东 教授 (同济大学)
时间地点: 2008年4月17日16:00-17:00 思源楼703
摘       要:  
报告题目: On the Brezis-Nirenberg Problem
报 告 人: 邹文明 教授 (清华大学)
时间地点: 2008年4月10日16:00-17:00 思源楼703
摘       要:  
2007年
报告题目: Degenerate elliptic equations:De Giorgi's conjectures
报 告 人: Prof. Xiao Zhong (University of Jyvaskyla, Finland)
时间地点: 2007年12月13日16:00-17:00 思源楼1013
摘       要: I will talk about the continuity of solutions of second order, linear, degenerate elliptic equations with divergence structure, and discuss the conjectures raised by De Giorgi.
报告题目: Clustered Bubbles for An Elliptic Problem with Critical Growth
报 告 人: Prof. Shusen Yan (School of Mathematics, Statistics and Computer Science,The University
of New England,Australia )
时间地点: 2007年12月6日16:00-17:00 思源楼703
摘       要:  
报告题目: Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms
报 告 人: Prof.Francois Murat (Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie (Paris VI), France)
时间地点: 2007年11月29日16:00-17:00 思源楼703
摘       要:  
报告题目: Global properties of the Ricci Flow on Open Manifolds
报 告 人: Prof. J. Eichhorn (University of Greifswald,Germany)
时间地点: 2007年9月20日16:00-17:00 思源楼1013
摘       要:  
报告题目: Schrodinger equation with multiparticle potential and Critical nonlinearity
报 告 人: Prof. Jan Chabrowski (University of Quennsland)
时间地点: 2007年9月20日15:00-16:00 思源楼1013
摘       要:  
报告题目: Compressible porous medium flow on bounded domain
报 告 人: Prof.Ronghua Pan (Georgia Institute of Technology, USA)
时间地点: 2007年6月21日16:00-17:00 思源楼712
摘       要: The problem is modeled by compressible Euler equations with frictional damping
with non-slip boundary condition. We construct global uniformly bounded weak
entropy solutions for the problem via compensated compactness. Furthermore,
the weak entropy solutions are shown to converge to steady states in large time.
This matches to the behavior of solutions for related porous medim equation. The talk is based on the joint work with K. Zhao .
报告题目: Formation of viscous shocks and asymptotic convergence of viscous approximations
报 告 人: Prof.Alberto Bressan (ICM一小时大会邀请报告人,Penn state University,USA)
时间地点: 2007年6月14日16:00-17:00 思源楼712
摘       要: Vanishing viscosity approximations are known to converge to the unique entropy weak solution, for scalar as well as for hyperbolic systems of conservation laws in one space dimension.When the limit solution is piecewise smooth, a natural question is whether these viscous approximations admit an asymptotic expansion in powers of the viscosity coefficient: $$u^\ve = u + \epsilon v_1 + \epsilon^2 v_2 + \cdots $$
In the neighborhood of a shock, a similar expansion can be given in terms of a stretched space variable, as in the classical paper of Goodman and Xin (1992).For the scalar case, we give a rigorous proof of the existence of these asymptotic expansions, also after shock interactions have taken place.The analysis is based on new estimates on the formation of a viscous shock. The possibility of a similar result in the case of hyperbolic systems will be discussed. This is a joint work with Carlotta Donadello (S.I.S.S.A., Trieste)
报告题目: Theory and Applications of Wavelet Bases
报 告 人: Prof.Rong-Qing Jia (University of Alberta, Canada)
时间地点: 2007年6月7日16:00-17:00 思源楼1013
摘       要: In this talk I will present some recent results of my research on wavelet
Bases and their applications.We develop a general theory of multiresolution analysis. This theory isessential for the construction of wavelet bases on bounded domains.In particular, we introduce discrete wavelets on intervals and demonstrate the superb performance of their applications to image processing.We construct a family of spline wavelets on the interval satisfyingthe homogeneous boundary conditions. Some of these wavelet bases are Successfully
applied to numerical solutions of biharmonic equations
报告题目: Can a species keep pace with a shifting climate ?
报 告 人: Prof. Henri Berestycki (Ecole des hautes études en sciences sociales - Paris)
时间地点: 2007年6月7日10:30-11:30 思源楼703
摘       要: We introduce a reaction-diffusion model to describe the dynamics of a biological population facing a climate shift. In this context, global warming is interpreted as a Northward shift of the favourable zone for a given species. In terms of the various parameters, the question is to know whether a given species is able to keep track with the climate change and how the latter affects the population size and distribution. The reaction-diffusion sheds a new light on these questions. This is joint work with Odo Diekman, Kees Nagelkerke and Paul Zegeling (Netherlands). I will also present extensions to higher dimensions, reporting on a joint work with Luca Rossi. These extensions involve nonlinear elliptic and parabolic equations in unbounded domains and generalized principal eigenvalues of elliptic operators.
报告题目: An extension to a theorem of Liouville and applications
报 告 人: Prof. Li Yanyan(Department of Mathematics, University of Rutgers, USA)
时间地点: 2007年6月4日9:00-10:00 思源楼712室
摘       要:  
报告题目: Heat flow of harmonic maps whose gradients belong to Lx
报 告 人: Prof. Wang Changyou (Department of Mathematics, University of Kentucky )
时间地点: 2007年6月1日10:30-11:30 思源楼703
摘       要: In this talk, the speaker will describe a class of heat flow of harmonic maps u with for n≥4 and show that it is smooth. In particular, for n≥3, if is the first singular time of the heat flow of harmonic maps
报告题目: The Heterogeneous Allen-Cahn Equation in a Ball: Solutions with Layers and Spikes
报 告 人: 杜一宏 教授 (澳大利亚新英格兰大学 )
时间地点: 2007年5月15日16:00-17:00 思源楼509
摘       要:  
报告题目: Singular Solutions of the Vlasov-Poisson System
报 告 人: 李 亦 教授 (Univ.of Iowa and Hunan Normal Univ. )
时间地点: 2007年5月15日15:00-16:00 思源楼712
摘       要:  
报告题目: The mass-critical nonlinear Schrodinger equation
报 告 人: Dr. Monica Visan (Institute for Advanced Study, Princeton) )
时间地点: 2007年5月10日16:00-17:00 思源楼1013
摘       要: We prove global well-posedness and scattering for the mass-critical NLS in higher dimensions for radial data at the critical regularity.
This is joint work with Terence Tao and Xiaoyi Zhang.
报告题目: Pressure representation and boundary regularity of the Navier-Stokes equations with slip boundary condition
报 告 人: Prof. Hyeong-Ohk Bae (Ajou University, Suwon, Korea)
时间地点: 2007年4月19日16:00-17:00 思源楼1013
摘       要:  
报告题目: Banach空间含间断项的方程解的存在性
报 告 人: 刘笑颖 教授(徐州师范大学)
时间地点: 2007年3月29日16:00-17:00 思源楼1013
摘       要:  
报告题目: Some uniform estimates for the Prescribed Scalar Curvature Equation
报 告 人: Dr. Samy Skander Bahoura(Paris VI University, France)
时间地点: 2007年3月15日16:00-17:00 思源楼712
摘       要:  
报告题目: Elliptic equations with nonlinearities having a linear bound
报 告 人: 刘兆理 教授(首都师范大学)
时间地点: 2007年3月1日16:00-17:00 思源楼703
摘       要:  
报告题目: Controllability of some nonlinear parabolic equations
报 告 人: Dr. Jinmyong Ri(Insitute of Mathematics Academy of Sciences, DPR Korea)
时间地点: 2007年2月8日16:00-17:00 思源楼712
摘       要:  
报告题目: Semilinear elliptic equations with indefinite nonlinearities
报 告 人: 蒋美跃 教授 (北京大学)
时间地点: 2007年1月25日16:00-17:00 思源楼703
摘       要:  
报告题目: Bounded Resonance Problem for Semilinear Elliptic Equations
报 告 人: 苏加宝 教授 (首都师范大学)
时间地点: 2007年1月11日16:00-17:00 思源楼703
摘       要: We study the existence and multiplicity of nontrivial solutions for Semilinear elliptic resonance problems with bounded nonlinearities with that the corresponding energy functional may lose compactness at any level. Morse theory, minimax methods and flow invariance Methods are invovled together. This is a joint work with Zhaoli Liu.
2006年
报告题目: Spherically Symmetric Isentropic Compressible Flows with Density-Dependent Viscosity Coefficients
报 告 人: 酒全森 教授 (首都师范大学)
时间地点: 2006年12月14日16:00-17:00 思源楼703
摘       要: We construct global weak solutions to the compressible Navier-Stokes equations with density-dependent viscosity coefficients when the initial data is large and spherically symmetric. We focus on the case where Those coefficients vanish on vacuum. The solutions are obtained as limits of solutions in annular regions between two balls, and the equations hold in The sense of distribution in the entire space-time domain. In particular.we
prove the existence of spherically symmetric solutions to the Saint-Venant model for shallow water.
报告题目: Nonrelativistic limit of a model problem in radiation hydrodynamics
报 告 人: 雍稳安 教授 (清华大学)
时间地点: 2006年12月7日16:00-17:00 思源楼703
摘       要: This talk is concerned with a model system for radiation hydrodynamics in multiple dimensions. The system depends singularly on the light speed c and consists of a scalar
nonlinear balance law coupled via an integral-type source term to a family of radiation Transport equations. We first show existence of entropy solutions to Cauchy problems of the model system in the framework of functions of bounded variation. This is done by using difference schemes and discrete ordinates.Then we establish strong convergence of the entropy solutions, indexed with c,as c goes to infinity. The limit function satisfies a scalar integro-differential equation.
报告题目: Fokker-Planck Equations in Complex Fluids
报 告 人: 张平文教授 (北京大学)
时间地点: 2006年11月30日16:00 思源楼703
摘       要: We are interested in the multi-scale physical model of complex fluid. Dumbbell and Rod-like model are one of the most typical models. In those models, the viscosity is thought of being brought by large amount of polymers in the Newtonian solvent. Each particle of polymers is assumed as an elastic dumbbell or a rod. This is a typical two-scale physical problem. In order to describe the motion of the polymers, we use a mesoscopic stochastic differential equation or Fokker-Planck (Smoluchowski) equation.
In this talk, I will focuse on the mathematical analysis of multi-scale models of complex fluids and the structure of stationary solutions of the Doi-Onsager equation.
报告题目: Numerical approximation of population balance equations in process engineering
报 告 人: Prof. Gerald Warnecke (Institut fuer Analysis und Numerik, Otto-von-Guericke-Universitaet )
时间地点: 2006年11月23日16:00 思源楼1013
摘       要:  
报告题目: On Fokker-Planck-Boltzmann equation near Maxewllian
报 告 人: 李海梁 教授 (首都师范大学)
时间地点: 2006年11月16日16:00 思源楼703
摘       要: In this talk, we consider the Fokker-Planck-Boltzmann equation viewed as the Boltzmann equation with additional diffusion term in velocity space to describe for instance the transportation in thermal bath of binary elastic collisional particles. The strong solution for initial data near an absolute Maxwellian is proven to exist globally in time. The effect of the diffusion in phase space is investigated. It produces a diffusion process in velocity space and results in a heating process on the macroscopic fluid-dynamical observable, and accelerates the convergence of solutions to the equilibrium of self-similar Maxwellian at the faster time-decay rate than Boltzmann equation. Moreover, the Fokker-Planck-Boltzmann equation is shown to converge under an appropriate scaling strongly to the Boltzmann equation in the process of zero diffusion limit.
报告题目: Time periodic solutions of the Boltzmann equation
报 告 人: Prof. Tong Yang (City University of Hong Kong)
时间地点: 2006年10月26日16:00 思源楼703
摘       要:  
报告题目: 大庆归来话电法测井
报 告 人: 李大潜院士 (复旦大学)
时间地点: 2006年10月17日(星期四)上午10:00-11:00 思源楼712
摘       要:  
报告题目: Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge
报 告 人: 李天虹 副研究员(数学与系统科学研究院)
时间地点: 2006年10月12日(周四) 下午4:00 -5:00 思源楼712
摘       要: It is well known that, when a supersonic Euler flow passes a straight wedge whose vertex angle less than the extreme angle, there exists a shock front Emanating from the wedge vertex.We study the $L^1$ well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge with small total variation of the tangent angle function. In this case, the Lipschitz wedge perturbs the flow and the waves reflect after interacting with the strong shock front or the wedge boundary . We first obtain the existence of solutions in $BV$ by the wave front tracking method. Then we study the uniqueness of the solutions. After studying the Lyapunov functional between two solutions and dealing with the boundary difficulty, the $L^1$ stability is established, so is the Uniqueness of the solutions by the wave front tracking method. Later we get uniqueness in a broader class, i.e.in the class of the viscosity solutions
报告题目: Initial-Boundary value problem for the Boltzmann equation
报 告 人: Prof.Shih-Hsien Yu (City University of Hong Kong, Hong Kong)
时间地点: 2006年9月28日(周四) 下午4:00 -5:00 思源楼712
摘       要: We will talk on the recent development on the Green's function for the Boltzmann equation. A separation of the physical scale in the space-time domain is introduced. With the decomposition, one could combine energy estimates and pointwise estimates to obtain an exponentially sharp global estimates on a solution of the initial-boundary value problem for the Boltzmann equation
报告题目: The Wigner-Fokker-Planck equation:large-time behavior and dispersive effects
报 告 人: Prof. Anton Arnold (Technische Universitaet Wien , Austria)
时间地点: 2006年9月21日(周四) 下午4:00 -5:00 思源楼709
摘       要: The Wigner-Poisson-Fokker-Planck (WPFP) system is a quantum kinetik equation that is being used for simulating nano-devices like the resonant tunneling diode. We shall first Discuss the linear Wigner-Fokker-Planck equation (wellposedness, large-time behavior). Those results will be the bases for analyzing the non-linear WPFP system. The key tool is a new a-priori estimate for the electric field which exploits the dispersive structure of this kinetic equation. This is an extension to quantum kinetics of strategies used by Perthame for the Vlasov-Poisson system.
报告题目: Nonlinear Fluiddynamic PDEs and Multiscale Analysis
报 告 人: 王术 教授(北京工业大学 )
时间地点: 2006年9月14日(周四) 下午4:00 -5:00 思源楼712
摘       要: In this talk asymptotic limits and multiscale analysis problems of some macroscopic Fluiddynamic partial differential equations are studied. These asymptotic limits conclude quasineutral limit and nonrelativistic limit etc. while the nonlinear Fluiddynamic PDEs concern some models like Euler-Maxwell system, e-MHD system, Euler-Poisson system, Navier-Stokes-Poisson system and Drift-Diffusion system etc, widely used in the area of applied sciences such as semiconductors, plasmas, fluid dynamics and so on, and they are full of multiscale phenomena. Some formal and rigorous convergence results are given and some new methods or ideas are reviewed
报告题目: On the free boundary problem of 3-D incompressible Euler equations
报 告 人: 章志飞 博士(北京大学)
时间地点: 2006年8月31日(周四) 下午4:00 -5:00 思源楼703
摘       要: In this talk, we will discuss in 3-D the motion of a general inviscid, incomepressible fluid with a free interface which separates the fluid region from the vacuum. We assume that the fluid region is below the vacuum and there is no surface tension on the free surface. Then we prove the local wellposedness of the free boundary problem in Sobolev space provided that there is no self-intersection point on the initial surface and under the stability assumption.
报告题目: Some Results of non-smooth divergence free transport
报 告 人: Prof. Tao Luo (Georgetown University, USA)
时间地点: 2006年8月17日(周四) 下午4:00 -5:00 思源楼703
摘       要: In this talk, we will survey some results on the uniqueness of the non-smooth Divergence free transport equation,including the results of Diperna-Lions and Ambrosion. Then we will present a counterexample of nonuniquness by Colombini, Rauch and myself..
报告题目: Spectral analysis near a threshold in geometric scattering
报 告 人: Prof. Xue-Ping Wang (Universite de Nantes, France)
时间地点: 2006年7月27日(周四) 下午4:00 -5:00 思源楼703
摘       要:  
报告题目: Computation of High Frequency Waves in Heterogeneous Media
报 告 人: Prof. Shi Jin (University of Wisconsin-Madison )
时间地点: 2006年7月20日(周四) 下午4:00 -5:00 思源楼703
摘       要: We introduce Eulerian methods that are efficient in computing high frequency waves through heterogeneous media. The method is based on the classical Liouville equation in phase space, with discontinous Hamiltonians (or singular coefficients) due to the barriers or material interfaces. We provide physically relavant interface conditions consistent with the correct transmissions and reflections, and then build the interface conditions into the numerical fluxes. This method allows the resolution of high frequency waves without numerically resolving the small wave lengths, and capture the correct transmissions and reflections at the interface. Moreover, we extend the method to include diffraction, and quantum barriers. Applications to semiclassical limit of linear Schrodinger equation, geometrical optics, elastic waves, and semiconductor device modeling, will be discussed.
当前位置:首页 > 学术报告 > 偏微分方程中心学术报告