A quasi Tikhonov regularization for a two-dimensional backward heat problem by a fundamental solution

作者：Cheng J; Liu J J^*

来源：Inverse Problems, 2008, 24(6): 065012.

DOI：10.1088/0266-5611/24/6/065012

Consider a two-dimensional backward heat conduction problem for a general domain D subset of R(2) with a C(2) boundary. Based on the fundamental solution to the heat equation, we propose to solve this problem by the boundary integral equation method, which generates a coupled ill-posed integral equation. Then the well posedness of the proposed regularizing problem and convergence property of the regularizing solution to the exact one are proven. Our regularizing scheme can be considered a quasi Tikhonov regularization, with the advantage of a relatively small amount of computation compared with the classical Tikhonov regularization. Numerical performances are given to show the validity of our inversion method.

• 出版日期2008-12
• 单位上海师范大学; 东南大学; 复旦大学