Abstract
A relationship between travel time, heat equation and exponential solutions for backward heat equation are discussed. For the purpose an inverse source problem and inverse boundary value problems for the heat equations are considered. Those problems employ a single set of the temperature and heat flux on a known boundary and finite time interval as the observation data and are to extract an information about the shape and location of an unknown discontinuity in a material with known conductivity :(1) heat source; (2) boundary; (3) interface. For the problems (1) in two space dimensions and (2), (3) in one space dimension some direct extraction formulae of the information are given by employing the enclosure method. The results suggest a relationship between the travel time of a virtual signal and the observation data. Some conjectures for the corresponding problems to (2) in multi space dimensions are formulated and discussed.
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