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 a semilinear parabolic equation is investigated. Moreover, for the approximate solution of this problem a first order of accuracy difference scheme is constructed. Existence and uniqueness results, and convergence estimates for the solution of this difference scheme are established. Considering a particular example, some numerical results are discussed.