An inverse medium problem for the heat equation

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 computation of a perturbation in this stratified medium having some information/knowledge about the temperature on the boundary of the domain due to heat flux applied to the same boundary. A linearized version of this inverse problem is considered and a linear integral equation is used for the numerical solution of the inverse problem. Some numerical examples are reported.