The direct and inverse problem for an inclusion within a heat-conducting layered medium

Abstract

This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously. ARTICLE HISTORY

The factorization method for recovering cavities in a heat conductor

“…The Newton iteration method is used in [3,6], and for the non-iterative algorithms, the reader is referred to the probe method [9] and the enclosure method [22,23] as well as the references therein. We would like to mention the linear sampling method developed recently in [15,19,[32][33][34]36] to reconstruct cavities and inclusions inside a heat conductor. Another kind of sampling-type method, known as the factorization method [28], is extended to locate the interface in a parabolic-elliptic equation [13].…”