|
2010年
|
| 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. |