Inverse problems in heat exchange processes

Abstract

This paper deals with an inverse problem concerning the identification of the heat exchange coefficient H (assumed depending on the temperature) between a certain material with the external environment (see, e.g., [2], [4] for real applications modelled with equations involving this coefficient). Only experimental measurements of the temperature are supposed to be known. The goal is to identify H in order to get a solution for the corresponding model, approximating same given temperature measurements. We begin by setting several scenarios for the inverse problem. For each scenario, we know the initial and ambient temperatures, identify function H through different methods and obtain error bounds in adequate norms (uniform and square integrable). Finally, we study the inverse problem in the framework of the classical theory for Hilbert spaces. Several methods are used (Tikhonov, Morozov, Landweber,...) and the approximations obtained, as well as the one provided by the previous algorithm, are shown.