A mollification regularization method for unknown source in time-fractional diffusion equation

Abstract

In the present paper, we consider an inverse source problem for a fractional diffusion equation. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We give the mollification regularization method to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, a new a posteriori parameter choice rule is also proposed and a good error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.