A quasi-boundary-value method for solving a nonlinear space-fractional backward diffusion problem

Abstract

In this paper, we adopt a quasi-boundary-value method to solve the nonlinear space-fractional backward problem with perturbed both final value and variable diffusion coefficient in general dimensional space, which is a severely ill-posed problem. The existence, uniqueness and stability of the solution for the quasi-boundary-value problem are proved. Convergence estimates are presented under an a-priori bound assumption of the exact solution. Finally, several numerical examples are given by the finite difference scheme and the fixed-point iteration method to show the effectiveness of the theoretical results.