A porous thermoelastic diffusion theory of types II and III

In this paper, we derive a nonlinear theory of thermoelasticity with voids and diffusion according to the Green–Naghdi theory of thermomechanics of continua 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. We prove the well-posedness of the linear model and the asymptotic behavior of the solutions by the semigroup theory of linear operators. Finally, we investigate the impossibility of the localization in time of solutions. The main idea to prove this result is to show the uniqueness of solutions for the backward in time problem.