Landweber iterative method for identifying a space-dependent source for the time-fractional diffusion equation

Boundary value problems

Dun-Gang Li¹  Yu-Peng Ren¹  Fan Yang¹  Xiao-Xiao Li¹ 

[1] School of Science, Lanzhou University of Technology, Lanzhou, P.R. China

关键词: time-fractional diffusion equation;    ill-posed problem;    unknown source;    Landweber iterative method;    35R25;    47A52;    35R30;   

DOI  :  10.1186/s13661-017-0898-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper is devoted to identifying an unknown source for a time-fractional diffusion equation with variable coefficients in a general bounded domain. This is an ill-posed problem. Firstly, we obtain a regularization solution by the Landweber iterative regularization method. The convergence estimates between regularization solution and exact solution are given under a priori and a posteriori regularization parameter choice rules, respectively. The convergence estimates we obtain are optimal order for any p in two parameter choice rules, i.e., it does not appear to be a saturating phenomenon. Finally, the numerical examples in the one-dimensional and two-dimensional cases show our method is feasible and effective.

【 授权许可】

CC BY