An inverse boundary value problem for identifying a time dependent inclusion for the heat equation

Gen Nakamura
Hokkaido University, Japan


Date: September 28, 2005

For a one space dimensional heat conductive medium with a time dependent unknown inclusion, we have developed a reconstruction procedure of the probe type method from the Neumann to Dirichlet map as a measurement. Most of the argument holds for higher space dimensions except the analysis of the behavior of the so called reflected solution which becomes very tedious for the higher space dimensional case. This problem originated from the study by Prof. V. Isakov et. al about the uniqueness of the identification not only for one space dimension. As for the associated reconstruction problem, as far as I know, this is the first attempt.