Study of a Cauchy problem with two parameters regularization framework

报告题目：Study of a Cauchy problem with two parameters regularization framework

报告时间：2023年11月3日（周五）下午4:30-5:30

报告地点：红瓦楼826

报告人：龚荣芳  教授（南京航空航天大学）

报告摘要：In this talk, we consider a Cauchy problem of recovering both missing value and flux on inaccessible boundary from Dirichlet and Neumann data measured on the remaining accessible boundary. With an introduction of a relaxation parameter, the Dirichlet boundary conditions are approximated by two Robin ones. Compared to the existing work, the regularity requirement for the Cauchy data in natural spaces are imposed on the boundary. Also, this makes the relaxation model more stable in the sense that the bigger the introduced parameter is, the smaller the condition number of the matrix involved in the reduced system is. Associated with two mixed boundary value problems, a regularized Kohn-Vogelius formulation is proposed. A series of theoretical results are established for the new reconstruction model. Several numerical examples are provided to verify the feasibility of the proposed method.

报告人简介：龚荣芳，南京航空航天大学数学学院，教授、博士生导师，计算科学系主任，江苏省计算数学分会常务理事、JSIAM理事，研究方向主要包括生物光、色谱和脑成像以及Cauchy问题等数学物理反问题的建模、正则化理论与方法，已在Numer. Math.、Inverse Probl.、CiCP、JCM等发表学术论文30篇。主持完成国家自然科学基金青年项目、江苏省自然科学基金等多项。当前主持国家自然科学基金面上项目和科技部外专项目各1项。

报告邀请人：刘可伋 教授