A bending theory of thermoelastic diffusion plates based on Green-Naghdi theory

Abstract

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.