A theory of thermoelasticity with diffusion under Green-Naghdi models

In this paper, we use the Green-Naghdi theory of thermomechanics of continua to derive a nonlinear theory of thermo-elasticity with diffusion of types II and III. This theory permits propagation of both thermal and diffusion waves at finite speeds. The equations of the linear theory are also obtained. With the help of the semigroup theory of linear operators we establish that the linear anisotropic problem is well posed and we study the asymptotic behavior of the solutions. Finally, we investigate the impossibility of the localization in time of solutions.