An iterative numerical method for an inverse source problem for a multidimensional nonlinear parabolic equation

Abstract

The main aims of this paper are to investigate the existence and uniqueness results for the solution of an inverse source problem for a multidimensional, semilinear, backward parabolic equation, subject to Dirichlet boundary conditions, and to propose an iterative difference scheme for the numerical solution of the problem. The unique solvability of the difference scheme is established, as well. In the foundation of the theoretical results, some tools and facts from the operator theory, contraction principle and the Banach fixed-point theorem are applied. Furthermore, a comprehensive numerical analysis and several illuminating visualizations are carried out by employing the iterative difference schemes proposed on some test problems.