Total variation regularization for recovering the spatial source term in a time-fractional diffusion equation
Abstract
In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational (TV) regularization. In contrast to the classical Tikhonov model incorporating penalty terms, the inclusion of a TV term proves advantageous in reconstructing solutions that exhibit discontinuities or piecewise constancy. The control problem is approximated by a fully discrete scheme, and convergence results are provided within this framework. Furthermore, a lineraed primal-dual iterative algorithm is proposed to solve the discrete control model based on an equivalent saddle-point reformulation, and several numerical experiments are presented to demonstrate the efficiency of the algorithm.
Cite
@article{arxiv.2310.12029,
title = {Total variation regularization for recovering the spatial source term in a time-fractional diffusion equation},
author = {Bin Fan},
journal= {arXiv preprint arXiv:2310.12029},
year = {2025}
}