Probing for inclusions in heat conductive bodies

Patricia Gaitan; Hiroshi Isozaki; Olivier Poisson; Samuli Siltanen; Janne Tamminen

doi:10.3934/ipi.2012.6.423

Article Contents

2012, Volume 6, Issue 3: 423-446. Doi: 10.3934/ipi.2012.6.423

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Probing for inclusions in heat conductive bodies

1.
Aix-Marseille University
2.
University of Tsukuba
3.
Aix-Marseille Université
4.
University of Helsinki

Received: September 2010

Revised: May 2012

Published online: September 2012

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Abstract

This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1--3 for probing the discontinuous part of the conductivity from local temperature and heat flow measurements at the boundary. The approach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is possible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering locations of discontinuities approximately from noisy data.

Keywords:

Mathematics Subject Classification: Primary: 35R30, 35K05; Secondary: 58J35.

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