Polynomial and exponential decay rates of a laminated beam system with thermodiffusion effects

Abstract

In this paper we consider a laminated beam system with thermodiffusion effects with two kinds of boundary conditions, in which the mass diffusion introduces a new critical thickness in addition to the conventional critical thickness of thermoelastic damping. By using the method of semigroup, we prove the system is global well posed. The polynomial stability is established by using frequency domain method if the wave speeds are nonequal. We also establish exponential decay of energy under the assumption of equal wave speeds. At last, we present some numerical experiments to illustrate our theoretical results. The result is new and is the first time when the stabilization of the laminated beam system with thermodiffusion effects is obtained.