Dissipativity conditions and inverse problems for heat conduction with linear memory

Abstract

The inverse problem of determining the heat capacity and thermal conductivity is studied for rigid and homogeneous heat conductors with linear fading-memory, when the heat flux and the temperature are known on the boundary. A uniqueness theorem is proved, for the inverse problem with overspecified data on the boundary, by using the Laplace transforms and the thermodynamic restrictions on the constitutive equations. Finally, the heat capacity and the thermal conductivity are determined when the domain occupied by the conductor is a half-plane.