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Two main aims of this paper are to develop a numerical method to solve aninverse source problem for parabolic equations and apply it to solve anonlinear coefficient inverse problem. The inverse source problem in this paperis the problem to reconstruct a source term from external observations. Ourmethod to solve this inverse source problem consists of two stages. We firstestablish an equation of the derivative of the solution to the parabolicequation with respect to the time variable. Then, in the second stage, we solvethis equation by the quasi-reversibility method. The inverse source problemconsidered in this paper is the linearization of a nonlinear coefficientinverse problem. Hence, iteratively solving the inverse source problem providesthe numerical solution to that coefficient inverse problem. Numerical resultsfor the inverse source problem under consideration and the correspondingnonlinear coefficient inverse problem are presented.

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