报告题目：uniqueness and numerical methods for inverse stokes problems
主 讲 人：杨家青 教授
单 位：西安交通大学
时 间：2024年5月16日20:00-21:00
腾 讯 id：399-163-522
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.
简 介：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。