Inverse boundary value problem for the heat equation with discontinuous coefficients

Gen Nakamura 1  and Satoshi Sasayama 2
  • 1 Department of Mathematics, Inha University, Incheon, 402-751, Korea
  • 2 Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

Abstract.

The inversion (= reconstruction) scheme, called the dynamical probe method, is applied to active thermography to identify unknown inclusions in an heat conductor and their physical properties. We assume the physical properties of the inclusions and heat conductor are isotropic and homogeneous. The measured data for the active thermography are the so-called Neumann to Dirichlet map. By defining some indicator function via the measured data, the identification is done by looking at the behavior of the indicator function. The underlying analysis is the short time asymptotic of fundamental solution of the heat equation with discontinuous coefficients.

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.

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