A thermoelastic diffusion theory with microtemperatures and microconcentrations

This article is concerned with a nonlinear theory of thermodynamics for elastic materials in which the particles are subjected to classical displacement, temperature, and mass diffusion fields and whose microelements possess microtemperatures and microconcentrations. The equations of the linear theory are also obtained. It is shown that there exists coupling between temperature, chemical potential, microtemperatures, and microconcentrations even for isotropic bodies. With the help of the semigroup theory of linear operators, we prove the well-posedness of the linear anisotropic problem and we study the asymptotic behavior of the solutions.