Asymptotic analysis for a shear beam model with thermoelastic diffusion damping

In this paper we investigate a shear beam model with two dissipative mechanism considering the effects of heat, which is modeled by Fourier’s law, and the diffusion, which is modeled by Fick’s law. We show the well-posedness of the new model. As well as, we demonstrate the exponentially stability of the system without assuming the condition of equal wave speeds. Furthermore, we develop a finite element scheme for the new model and prove the energy decay of the system. Finally, we validate our results graphically through numerical simulations.