A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem

Phuong Mai Nguyen, Loc Hoang Nguyen

Published 2019-03-25Version 1

The aim of this paper is to solve an inverse source problem for parabolic equations. This is the problem to reconstruct a source term from external observations. Our method to solve this inverse source problem consists of two stages. We first establish an equation of the derivative of the solution to the parabolic equation with respect to the time variable. Then, in the second stage, we solve this equation by the quasi-reversibility method. The inverse source problem considered in this paper is the linearization of a nonlinear coefficient inverse problem. Hence, iteratively solving the inverse source problem provides the numerical solution to that coefficient inverse problem. Numerical results for the inverse source problem under consideration and the corresponding nonlinear coefficient inverse problem are presented.