AN INVERSE MEDIUM PROBLEM FOR THE HEAT EQUATION

Abstract

In the article we consider the two-dimensional heat equation in a circular domain where the thermal diffusivity is a piecewise constant function in the radial directon and is a constant function in the angular direction. In particular we consider the problem of the computation of a perturbation in this stratified medium having some knowledge about the temperature on tine boundary of the domain due to a heat flux applied to the same boundary. A linearized version of this inverse problem is considered and a numerical method to solve the corresponding linear inverse problem is proposed. This numerical method is based on a linear integral equation. Some numerical examples are reported.