Existence and Uniqueness Results for an Inverse Problem for Semilinear Parabolic Equations

Abstract

In the present study, unique solvability of an inverse problem governed by semilinear parabolic equations with an integral overdetermination is investigated. Furthermore, for the approximate solution of this problem a first order of accuracy difference scheme is constructed. Existence and uniqueness results for the solution of this difference scheme are established. Considering a particular example, some numerical results are discussed.