Analysis of the thermoviscoelastic Timoshenko system with diffusion effect

Abstract

This paper is concerned with a new Timoshenko beam model with thermal, mass diffusion and viscoelastic effects. First, by the C0-semigroup theory, we prove the well posedness of the considered problem with Dirichlet boundary conditions. An exponential decay is obtained by construction of the Lyapunov functional. Finally, a numerical study is done based on P1-finite element approximation for space discretization and implicit Euler scheme for time discretization, where we study the stability of the scheme, analysis of the error and obtained some numerical simulations.

Keywords

• Timoshenko type systems
• Thermodiffusion effects
• Well-posedness
• Stability
• Numerical results
• Error