Iteratively Regularized Gradient Method for Determination of Source Terms in a Linear Parabolic Problem

This paper investigates a numerical computation for determination of source terms in a linear parabolic problem. The source term is defined in the linear parabolic equation and Robin boundary condition from the measured final data and the measurement of the temperature in a subregion. We demonstrate how to compute Fréchet derivative of Tikhonov functional based on the solution of the adjoint problem. Lipschitz continuity of the gradient is proved. Iteratively regularized gradient method is applied for numerical solution of the problem. We conclude with several numerical tests by using the theoretical results.