Asymptotic stability for thermodiffusion Timoshenko systems of type III

Abstract

In this article, we study a Timoshenko model with thermal and mass diffusion effects. Heat and mass exchange with the environment during thermodiffusion in Timoshenko beam, where the heat conduction is given by Green and Naghdi, called thermoelasticity of type III. We obtain the stability of the system using the perturbed energy method and the system is exponentially stable when the wave speeds are equal. In the case of unequal wave speeds, we demonstrate that the system lacks exponential stability, and it is polynomially stable. These results indicate that the wave speed has a significant impact on the stability of the system, and the transmission performance of the system is better when the wave speeds are equal.

Keywords

• timoshenko system
• exponentially stable
• polynomially stable
• exponential stability
• thermodiffusion of type iii