On recovering space or time-dependent source functions for a parabolic equation with nonlocal conditions

Abstract

The paper studies inverse source problems for a parabolic equation with nonlocal initial and boundary conditions. The specificity of these problems is that the identifiable coefficients depend on only space or time variable. A numerical method for solution to problems is proposed based on reducing the initial problems to the parametric inverse problems with respect to ordinary differential equations using the method of lines. Then, we propose a non-iterative method based on using a special representation of the solutions to the obtained problems. We prove the existence and uniqueness of their solutions, and substantiate the existence of special representation of the solutions to these problems. Computation schemes, formulae, and the results of numerical experiments on test problems are provided.