| 报告题目： | Coefficient Identification Problems in Elliptic Equations |
| 报 告 人： | Prof. Dr. Dinh Nho Hao |
| Hanoi Institute of Mathematics, Vietnam\\ University of Leeds, UK | |
| 报告时间： | 10月1日下午2:00 |
| 报告地点： | 数学系九龙湖第一学术报告厅 |
| 相关介绍： | Abstract: We investigate the convergence rates for Tikhonov regularization of the problem of identifying the coefficient $q$ in the Neumann problem for an elliptic system. This problem is frequently arising in practice, for example, in ground water engineering. However, it is nonlinear and ill-posed. In the literature, researchers are using the least squares method for solving it and so they are faced with non-convex ill-posed optimization problems. In contrast, we regularize the problem by minimizing some new convex functionals over the admissible set. Taking the solutions of these optimization problems as the regularized solutions to the identification problem, we obtain the convergence rates of them correspondingly to 1) $q^*$-minimum norm solution, 2) a total variation-minimizing solution in the sense of the Bregman distance, or 3) a total variation-minimizing solution both in the sense of Bregman distance and $L^2$-norm under relatively simple source conditions without the smallness requirement on the source functions. We also study the convergence of the finite element method for this inverse problem. Some numerical results are presented. About the speaker: Prof. Dinh Nho Hao is a famous mathematician working on applied maths and computational Maths. He got his Ph.D on Mathematics in Germany in 1992. Now his research interests cover scientific computations, regularizing mehtods for ill-posed problems, numerical methods for image process. Now he is Marie Curie incoming international fellow, and the editors for several SCI journals such as Applied Numerical Mathematics, Inverse Problems in Science and Engineering, J. Inverse and Ill-posed Problems. |
