In this paper we examine the inverse problem of determining the amount of corrosion/disbonding which has occurred on the boundary of a single circular (or nearly circular) inclusion D in a two dimensional domain W using Cauchy data for the steady-state heat equation. We develop an algorithm for reconsructing a function which qunatifies the level of corrosion/disbonding at each point in ¶W. We also address the issue of well-posedness and develop a simple regularization scheme. Then we provide several numerical examples. We shall show a simple procedure for recovering the center of D assuming that the boundary of W and D have the same thermal conductivity.
Christian, Nicholas and Johnson, Mathew A., "Non-Destructive Testing of Thermal Resistances for a Single Inclusion in a 2-Dimensional Domain" (2004). Mathematical Sciences Technical Reports (MSTR). 42.