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.

Keywords:

• Inverse problem
• heat conduction
• layered medium
• boundary integral equation
• linear sampling method

AMS Subject Classifications:

• 45Q05
• 35K05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is supported by NSFC [grant number 11401241], [grant number 61374085]; by the Fundamental Research Funds for the Central Universities [grant number CZQ15020]. The second author is supported by NSFC [grant number 11171127], [grant number 11571132].