Lord-Shulman Thermoelasticity with Microtemperatures

In this paper we consider the Lord-Shulman thermoelastic theory with porosity and microtemperatures. The new aspect we propose here is to introduce a relaxation parameter in the microtemperatures. Then we obtain an existence theorem for the solutions. In the case that a certain symmetry is satisfied by the constitutive tensors, we prove that the semigroup is dissipative. In fact, an exponential decay of solutions can be shown for the one-dimensional case. In the last section, we restrict our attention to the case where we have an isotropic and homogeneous material without porosity effects and assuming that two of the constitutive parameters have the same sign. We see that the semigroup is dissipative.