Simultaneous inversion for the diffusion and source coefficients in the multi-term TFDE

摘要

This article deals with an inverse problem of determining the space-dependent diffusion coefficient and the source coefficient simultaneously in the multi-term time fractional diffusion equation (TFDE in short) using measurements at one inner point. From a view point of optimality, solving the inverse problem is transformed to minimize an error functional with the help of the solution operator from the unknown to the additional observation. The solution operator is nonlinear but it is of Lipschitz continuity by which existence of a minimum to the error functional is obtained using Sobolev embedding theorems. The homotopy regularization algorithm is introduced to solve the simultaneous inversion problem based on the minimization problem, and numerical examples are presented. The inversion solutions give good approximations to the exact solutions demonstrating that the homotopy regularization algorithm is efficient for the simultaneous inversion problem arising in the multi-term TFDE.