Qualitative results for a mixture of Green-Lindsay thermoelastic solids

We study qualitative properties of the solutions of the system of partial differential equations modeling thermomechanical deformations for mixtures of thermoelastic solids when the theory of Green and Lindsay for the heat conduction is considered. Three dissipation mechanisms are proposed in the system: thermal dissipation, viscosity effects on one constituent of the mixture and damping in the relative velocity of the two displacements of both constituents. First, we prove the existence and uniqueness of the solutions. Later we prove the exponential stability of the solutions over the time. We use the semigroup arguments to establish our results.