On an inverse boundary problem for the heat equation when small heat conductivity defects are present in a material

Abstract

For the heat equation in a bounded domain we consider the inverse problem of identifying locations and certain properties of the shapes of small heat‐conducting inhomogeneities from dynamic boundary measurements on part of the boundary and for finite interval in time. The key ingredient is an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements. Our approach is expected to lead to very effective computational identification algorithms.