Determination of the coefficient of thermal conductivity and heat capacity per unit volume in a multilayer medium

Abstract

We consider the inverse problem of simultaneously determining two time-dependent thermophysical characteristics—the coefficient of thermal conductivity and the heat capacity per unit volume—for a body having the shape of a layer situated between two other layers with known thermophysical characteristics. The necessary measurements are carried out on their outside boundaries. The problem is reduced to a system of nonlinear equations for which the existence of a solution is established by using Schauder's fixed-point theorem. We find conditions that guarantee that the solution of the inverse problem is unique.