Exponential decay in thermoelastic materials with voids and dissipative boundary without thermal dissipation

We study the energy decay of the solutions of a linear homogeneous anisotropic porous thermoelastic system in the context of Green and Naghdi model of type II with a boundary condition with memory for the displacement. By introducing a boundary free energy , we prove that, if the memory kernel exponentially decays in time, then also the energy exponentially decays when the porosity viscosity is present.