Identifying a diffusion coefficient in a time-fractional diffusion equation
Identifying a diffusion coefficient in a time-fractional diffusion equation
复制标题
确定时间分数扩散方程中的扩散系数
DOI：
10.1016/j.matcom.2018.03.006
复制
发表时间：
2018-09-01
影响因子：
4.6
通讯作者：
Li, Y. S.
中科院分区：
文献类型：
--
作者：
Wei, T.;Li, Y. S.
In this paper, we propose a conjugate gradient algorithm for identifying a space-dependent diffusion coefficient in a time-fractional diffusion equation from the boundary Cauchy data in one-dimensional case. The existence and uniqueness of the solution for a weak form of the direct problem are obtained. The identification of diffusion coefficient is formulated into a variational problem by the Tikhonov-type regularization. The existence, stability and convergence of a minimizer for the variational problem approach to the exact diffusion coefficient are provided. We use a conjugate gradient method to solve the variational problem based on the deductions of a sensitive problem and an adjoint problem. We test three numerical examples and show the effectiveness of the proposed method. (C) 2018 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
