Identification of source terms in heat equation with dynamic boundary conditions

Abstract

We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is analyzed, especially a gradient formula of the functional is proved and given in terms of the solution of an adjoint problem. Next, the existence and uniqueness of a quasi‐solution are also investigated. Finally, the numerical reconstruction of some heat sources in a 1‐D equation is presented to show the efficiency of the proposed algorithm.