Recovering the time-dependent potential function in a multi-term time-fractional diffusion equation

摘要

In the present paper, we devote our effort to a nonlinear inverse problem for recovering a time-dependent potential term in a multi-term time-fractional diffusion equation from the boundary measured data. First we study the existence, uniqueness and regularity of solution for the direct problem by using the fixed point theorem. Then a stability estimate of inverse coefficient problem is obtained based on the regularity of solution of direct problem and some generalized Gronwall's inequalities. Numerically, we reformulate the inverse potential function into a variational problem, and we use a Levenberg-Marquardt method to find the approximate potential function. Numerical experiments for five examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.