Prescribing a heat flux coming from a wave equation

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.

19 pages, the final version

References in corpus (3)

• The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator
• An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method
• On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body

Cited by in corpus (3)

• Extracting discontinuity using the probe and enclosure methods
• The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell type initial data
• The enclosure method for the heat equation using time-reversal invariance for a wave equation