  In the present paper, we study a linear thermoelastic porous material with a
constitutive equation for heat flux with memory. An approximated theory of
thermodynamics is presented for this model and a maximal pseudo free energy is
determined. We use this energy to study the spatial behaviour of the
thermodynamic processes in porous materials. We obtain the domain of influence
theorem and establish the spatial decay estimates inside of the domain of
influence. Further, we prove a uniqueness theorem valid for finite or infinite
body. The body is free of any kind of a priori assumptions concerning the
behaviour of solutions at infinity.
