On Tikhonov's method and optimal error bound for inverse source problem for a time-fractional diffusion equation

摘要

We investigate the linear but ill-posed inverse problem of determining a multidimensional space-dependent heat source in a time-fractional diffusion equation. We show that the problem is ill-posed in the Hilbert scale H-r(R-n) and establish global order optimal lower bound for the worst case error. Next, we use the Tikhonov regularization method to deal with this problem in the Hilbert scale H-r(R-n). Locally optimal choices of parameters for the family of regularization operator in the Hilbert scales H-r(R-n) are analyzed by a-priori and a-posteriori methods. Numerical implementations are presented to illustrate our theoretical findings. (C) 2020 Elsevier Ltd. All rights reserved.