An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method

Masaru Ikehata; Mishio Kawashita

doi:10.3934/ipi.2014.8.1073

Article Contents

2014, Volume 8, Issue 4: 1073-1116. Doi: 10.3934/ipi.2014.8.1073

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An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method

Masaru Ikehata^1, and
Mishio Kawashita^2,

1.
Laboratory of Mathematics, Institute of Engineering, Hiroshima University, Higashi Hiroshima 739-8527
2.
Department of Mathematics, Graduate School of Sciences, Hiroshima University, Higashi Hiroshima 739-8526

Received: November 30, 2013

Revised: September 30, 2014

Published: October 2014

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Abstract

This paper studies a prototype of inverse initial boundary value problems whose governing equation is the heat equation in three dimensions. An unknown discontinuity embedded in a three-dimensional heat conductive body is considered. A single set of the temperature and heat flux on the lateral boundary for a fixed observation time is given as an observation datum. It is shown that this datum yields the minimum length of broken paths that start at a given point outside the body, go to a point on the boundary of the unknown discontinuity and return to a point on the boundary of the body under some conditions on the input heat flux, the unknown discontinuity and the body. This is new information obtained by using enclosure method.

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Mathematics Subject Classification: Primary: 35R30, 35K05; Secondary: 80A23.

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References

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