On the identification of a thermal expansion coefficient

Abstract

In this paper, we identify a time-dependent thermal expansion function when some information about the temperature is known. This inverse problem is motivated by models that arise in food engineering. In particular, the model studied here describes high-pressure processes and it is governed by the heat equation with Robin boundary conditions in a cylindrical spatial domain. We study the inverse problem, proving a uniqueness result and obtaining a numerical scheme to compute the thermal expansion function. Several numerical examples are shown.