On the numerical solutions of some identification problems for one- and multidimensional parabolic equations backward in time

Abstract

In this paper, an abstract (differential) inverse problem backward in time, that is a class of some identification problems for simultaneous determination of the source and initial condition, is considered. A finite difference scheme is constructed for the numerical solution of this abstract problem. Some stability and almost coercive stability estimates for the constructed difference scheme are established by the tools of operator theory. Furthermore, the proposed abstract difference scheme and the acquired results for that are extended for several applications involving identification problems for one-and multidimensional parabolic equations. Finally, sundry illustrative numerical results and visualizations are carried out and discussed.(c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.