Extracting discontinuity in a heat conductive body. One-space dimensional case

Abstract

Three inverse boundary value problems for the heat equations in one-space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a material with a smooth heat conductivity by employing a single set of the temperature and heat flux on a known boundary as the observation data. Some extraction formulae of those discontinuities which suggest a relationship between the travel time of a virtual signal and the observation data are given by applying the enclosure method to the problems.

Keywords:

• Heat equation
• Inverse boundary value problem
• Thermal imaging
• Cavity
• Corrosion
• Interface
• AMS Subject Classifications
• 35R30
• 80A23

Acknowledgements

This research was partially supported by Grant-in-Aid for Scientific Research (C) (No. 18540160) of Japan Society for the Promotion of Science. The author would like to thank Mikhail Belishev for remarks about the relationship between the response operator and our observation data for the heat equation in one-space dimension and comments on our results in the earlier version of this article.