Uniqueness and existence theorems in thermoelasticity with voids without energy dissipation

Abstract

In this paper we investigate some qualitative aspects of the solutions of a new theory of thermoelasticity with voids based on the concept of volume fraction derived by Cicco and Diaco [A theory of thermoelasticity with voids without energy dissipation, J. Thermal Stresses 25 (2002) 493–503]. This theory has been established in the frame work of linear thermoelasticity without energy dissipation. The theory permits the propagation of heat as thermal waves at finite speed. By means of the logarithmic convexity method a uniqueness theorem is proved. With the help of the semigroup theory of linear operators an existence result is obtained.