Qualitative aspects in the coupled theory of thermoelastic diffusion

In this paper we derive some qualitative results of the coupled theory of thermoelastic diffusion for anisotropic media. We establish a reciprocity relation, which involves two thermoelastic diffusion processes at different instants. We show that this relation can be used to obtain reciprocity, uniqueness and continuous dependence theorems. The reciprocity theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. The uniqueness theorem is derived without the positive definiteness assumption on the elastic, conductivity and diffusion tensors. We prove also that the reciprocal relation leads to a continuous dependence theorem studied on external body loads. Finally, we prove the existence of a generalized solution by means of the semigroup of linear operators theory.