A hybrid regularization method for simultaneous inversion of source term and initial value in a time-fractional diffusion equation

Abstract

This paper considers an inverse problem to find the space-dependent source term and initial data simultaneously in a time-fractional diffusion equation. This inverse problem is usually ill-posed, that is, small errors in the measurement typically lead to large errors in the solution. First, we give the conditional stability results about two unknown values. Then, a hybrid regularization method is used to obtain regularization solution. In the theoretical results, a priori parameter choice rule is proposed and convergence estimation is obtained. Finally, several typical numerical examples are shown to verify the effectiveness and accuracy of our suggested method.