Inverse boundary value problem for the heat equation with discontinuous coefficients

Abstract

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.