时间分数阶方程正反问题系列报告（一）：A relaxation model for Cauchy problem of elliptic diffusion equation

发布时间：2023-09-14 作者：浏览次数：

Speaker:	龚荣芳	DateTime:	2023年9月23日（周六）上午9:10-9:55
Brief Introduction to Speaker: 龚荣芳，南京航空航天大学理学院，教授，硕士生导师。2009年6月于浙江大学数学学院计算数学专业获理学博士学位，2009年6月起任职于南京航空航天大学理学院数学系。研究方向为医学成像、图像处理、参数识别和最优控制等数学物理反问题的正则化理论与数值方法。先后主持完成国家自然科学基金青年基金1项、国家博士后基金1项、江苏省自然科学基金青年基金1项、江苏省博士后基金1项、江苏省中央高校基础研究基金青年创新基金3项，当前主持国家自然科学基金面上项目1项，参与国家自然科学基金面上项目1项。在Numerische Mathematik、Inverse Problems、Inverse problems and Imaging、Communications in Computational Physics等期刊上发表SCI论文近30篇。		Place:	6号楼2楼报告厅
Abstract: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, 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. A series of theoretical results are established for the relaxation model based problem. Several numerical examples are provided to verify the feasibility of the proposed method.