Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method

摘要

In this paper, we consider the backward problem for diffusion equation with space-fractional Laplacian. In order to overcome the ill-posedness of the backward problem, we propose a fractional Tikhonov regularization method to solve it. Based on the conditional stability estimate and ana posterioriregularization parameter choice rule, the convergence rate estimate is presented undera-prioribound assumption for the exact solution. Finally, several numerical examples are given to show that the proposed numerical methods are effective.