Asymptotic behavior and numerical analysis for a Timoshenko beam with viscoelasticity and thermodiffusion effects

We study the qualitative and numerical behavior of a thermodiffusion Timoshenko beam with Kelvin–Voigt damping. The model, recently derived by Aouadi $ \rm et al. (2019), describes effects under classical Fourier's Fick's laws for heat mass diffusion transmission, respectively. With help semigroup theory linear operators, we prove well posedness considered problem. Without assuming well-known condition equal wave speeds, it is shown that associated C_0 $-semigroup to fully viscoelastic system analytic. Exponential stability impossibility localization solutions in time are immediate consequences. Two partial systems be polynomially or exponentially stable. approach based on Gearhart–Herbst–Prüss–Huang theorem used show lack exponential stability, whereas optimal polynomial decay rate can using Borichev & Tomilov's Theorem. Finally, propose spectral discretization method discrete energy decays otherwise.