On the spatial decay of solutions in the theory of swelling porous thermoelastic soils

In this paper we consider the linear theory of swelling porous thermoelastic soils. The formulation belongs to the general theory of mixtures for porous elastic solids filled with fluid and gas with thermal conduction and by considering the time derivative of temperature as a variable in the set of constitutive equations. The spatial decay is studied for the solutions of the initial-boundary value problems associated with the swelling theory of porous thermoelastic soils. Appropriate estimates are established for describing the spatial behaviour by means of a first-order differential inequality. The method of proof is based on the time-weighted method applied in appropriate classes of solutions.