讲座主题：Uniqueness and numerical methods for inverse Stokes problems

专家姓名：杨家青

工作单位：西安交通大学

讲座时间：2024年05月29日15:00-16:00

讲座地点：数学与信息科学学院341

主办单位：hy590海洋之神平台数学与信息科学学院

内容摘要：

In this talk, we consider an inverse Stokes problem in a bounded domain with a discontinuous viscosity coefficient. By analyzing the singularity of the Dirichlet Green's function near the interface in combination with constructing a well-posed Stokes-Brinkman system in a small domain, we prove a global uniqueness theorem that the discontinuous viscosity coefficient can be determined by the local Dirichlet-to-Neumann map defined on an arbitrary small open subset of the boundary. Moreover, we also consider an inverse Stokes problem of reconstructing a bounded solid in an unbounded Stokes fluid, where the well-known LSM, FM and GLSM are extended from the wave equation into the Stokes equation by only taking the velocity fields in a certain domain. Finally, some numerical results are presented to illustrate the effectiveness of the inversion algorithms.

主讲人介绍：

杨家青，西安交通大学数学与统计学院教授/博导，研究方向为反问题的数学理论与计算方法。目前，在SIAM J. Appl. Math., SIAM J.Numer. Anal., SIAM J. Sci.Comput., SIAM J. Imaging Sci., JCP，JDE，IPI等国际期刊发表论文近四十篇。主持国家自然科学基金优秀青年科学基金项目，是国家重点研发计划的课题负责人；曾获陕西省百人计划青年项目、中国工业与应用数学学会“CSIAM应用数学青年科技奖”；山东省自然科学二等奖等。