Abstract

In this talk, we revisit 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, weaker regularity is required on the Dirichlet data. This makes the proposed model simpler and more efficient in computation. Associated with two mixed boundary value problems, a regularized Kohn-Vogelius formulation is proposed, which leads to a regularization framework with two regularization parameters. 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.

Biography

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、江苏省工业与应用数学学会理事，研究方向主要包括光学成像、脑成像、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.、IPI、CMAME、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高端外国专家项目各1项，参与国家面上项目和科技部“LJ”专项各1项。