  This article is concerned with bending plate theory for thermoelastic
diffusion materials under Green-Naghdi theory.
  First, we present the basic equations which characterize the bending of thin
thermoelastic diffusion plates for type II and III models. The theory allows
for the effect of transverse shear deformation without any shear correction
factor, and permits the propagation of waves at a finite speed without energy
dissipation for type II model and with energy dissipation for type III model.
By the semigroup theory of linear operators, we prove the well-posedness of the
both models and the asymptotic behavior of the solutions of type III model. For
unbounded plate of type III model, we prove that a measure associated with the
thermodynamic process decays faster than an exponential of a polynomial of
second degree.
  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.
