Identification of the thickness of a thin layer from boundary measurements

Abstract

The aim of this paper is the identification of the thickness of a highly conductive thin layer from boundary measurements. In the introduction, we propose an asymptotic model of the stiff transmission problem. In this context, the thickness of the thin layer appears to be a parameter of the boundary condition of a Ventcel equation. Our goal is to prove the identifiability of this parameter from boundary measurements. After studying the regularity of the direct problem for non-smooth data, identifiability and weak stability results are proved by introducing a suitable admissible parameter space. Numerical experiments are given to illustrate the results.