On the time decay of solutions in porous-thermo-elasticity of type II

Abstract

In this paper we investigate the asymptotic behaviour of thesolutions of the linear theory of thermo-porous-elasticity. That is,we consider the theory of elastic materials with voids when the heatconduction is of type II. We assume that the only dissipationmechanism is the porous dissipation. First we prove that,generically, the solutions are exponentially stable on time or, inother words, the decay of solutions can be controlled by a negative exponential for a generic class of materials. The reason lies in the fact that the temperature is strongly coupled with both the microscopic and macroscopic structures of the materials and plays the roleof a 'driving belt' between the dissipation at the microscopicstructure and the macroscopic one. Later we note that the decay ofsolutions cannot be fast enough to make the solutions be zero in afinite period of time. Finally, we show that when the coupling termbetween the microscopic (or macroscopic) structure and the thermalvariable vanishes, the solutions do not decay exponentially(generically).