Identifiability and stability results of one emerging crack in heterogeneous media by one boundary measurements

Abstract

SUMMARYWe consider the inverse problem of determining one emerging crack in a plane heterogeneous medium. We show that one measurement on a part of the boundary with appropriate ux uniquely determines such a crack. We further establish a local Lipschitz continuity result. At the end, we give an approximation result for the nonstationary heat equation.