A new regularization method for solving a time-fractional inverse diffusion problem |
| |
Authors: | GH Zheng |
| |
Institution: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China |
| |
Abstract: | In this paper, we consider an inverse problem for a time-fractional diffusion equation in a one-dimensional semi-infinite domain. The temperature and heat flux are sought from a measured temperature history at a fixed location inside the body. We show that such problem is severely ill-posed and further apply a new regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under the a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective. |
| |
Keywords: | Regularization method Caputo's fractional derivatives Temperature Heat flux Fourier transform Laplace transform |
本文献已被 ScienceDirect 等数据库收录! |