On the uniqueness and continuous data dependence of solutions in the theory of swelling porous thermoelastic soils

This paper studies the uniqueness and continuous data dependence of solutions of the initial-boundary value problems associated with the linear theory of swelling porous thermoelastic soils. The formulation belongs to the 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. Some uniqueness and continuous data dependence results are established under mild assumptions on the constitutive constants. Thus, it is shown that the general approach of swelling porous thermoelastic soils is well posed. The method of proof is based on some integro-differential inequalities and some Lagrange–Brun identities.