Travel Time and Heat Equation. One space dimensional case II

Details Travel Time and Heat Equation. One space dimensional case II Travel Time and Heat Equation. One space dimensional case II

2006-11-15

arxiv.org/abs/math/0611449v1

Mathematics

Analysis of PDEs

27pages

Scientific paper

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 {\it virtual} signal and the observation data are given by applying the enclosure method to the problems.

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