On the unique solvability of an inverse problem for a semilinear equation with final overdetermination

Abstract

This paper deals with existence and uniqueness of the solution of an inverse problem for a semilinear equation subject to a final overdetermination in a Banach space. Moreover, the first order of accuracy Rothe difference scheme is presented for the numerical solution of this problem. The existence and uniqueness result for this difference scheme is given. This difference scheme is applied on a particular example and some numerical results are given.