The iterative generalized quasi‐boundary value method for an inverse source problem of time fractional diffusion‐wave equation in a cylinder

Abstract

This paper is devoted to solve an inverse source problem of time fractional diffusion‐wave equation in a cylinder. The ill‐posedness, existence, and uniqueness of the inverse source problem are proved. We propose an iterative generalized quasi‐boundary value regularization method to deal with the inverse source problem. The convergence rates of the regularized solution are obtained under the a priori regularization parameter choice rule and the a posteriori regularization parameter choice rule. Numerical examples are presented to show the validity and stability of the proposed method.