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

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 {\it 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.

References in corpus (1)

• Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

Cited by in corpus (5)

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• Extracting discontinuity using the probe and enclosure methods
• Prescribing a heat flux coming from a wave equation
• The enclosure method for the heat equation using time-reversal invariance for a wave equation