Prescribing a heat flux coming from a wave equation
Masaru Ikehata
TL;DR
This paper investigates the effects of prescribing a heat flux proportional to the wave equation's Neumann data on a heat conductive body, revealing differences in asymptotic behavior relevant to cavity detection.
Contribution
It introduces a novel analysis of the time domain enclosure method's asymptotic behavior when heat flux is linked to wave equation data.
Findings
Identifies differences in asymptotic behavior of the indicator function
Enhances understanding of cavity detection via heat flux analysis
Provides theoretical insights into wave-heat interaction
Abstract
What happens when one prescribes a heat flux which is proportional to the Neumann data of a solution of the wave equation in the whole space on the surface of a heat conductive body? It is shown that there is a difference in the asymptotic behaviour of the indicator function in the most recent version of the time domain enclosure method, which aims at extracting information about an unknown cavity embedded in the body.
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