Speaker: 王海兵教授，东南大学
Inviter: 张海文
Title: Enhanced inversion schemes for inverse problems of diffusion equations utilizing multitemporal observations
Language: Chinese
Time & Venue: 2026.3.29 15:00-16:00 南楼N613
Abstract: In this talk, we present our recent results on inverse problems for diffusion equations leveraging multitemporal observations. Our first focus is recovering nonsmooth initial status in linear convection-diffusion equations. We introduce a novel offline data assimilation approach that incorporates an anisotropic total variation seminorm into the classical 4D-Var framework, alongside a new minimization algorithm that facilitates sequential observation assimilation. Next, we tackle the reconstruction of nonsmooth diffusion coefficients. To handle the associated nonlinearity, we utilize an adaptive Kaczmarz-type Nesterov method, providing a rigorous convergence analysis with clearly defined assumptions and parameter selections. The performance of both proposed schemes is validated through extensive 2D and 3D numerical experiments,
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