A modified regularization method for a Cauchy problem for heat equation on a two-layer sphere domain

作者：Xiong, Xiangtuan^*; Cao, Xiaoxiao; He, Shumei; Wen, Jin

来源：Applied Mathematics and Computation, 2016, 290: 240-249.

DOI：10.1016/j.amc.2016.06.004

• Ill-posed problem
• Radially symmetric inverse heat conduction problem
• Error estimate
• Modified Tikhonov regularization

In this paper, we study a non-characteristic Cauchy problem for a radially symmetric inverse heat conduction equation in a two-layer domain. This is a severely ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. It is well-known that the classical Tikhonov regularization solutions are too smooth and the approximate solutions may lack details that might be contained in the exact solutions. Combining Fourier transform technique with a modified version of the classical Tikhonov regularization, we obtain a regularized solution which is stably convergent to the exact solution with a sharp error estimate.

• 出版日期2016-11-1
• 单位西北师范大学