Bresse-Timoshenko type systems with thermodiffusion effects: Well-possedness, stability and numerical results

TL;DR

This paper analyzes a Bresse-Timoshenko beam model incorporating thermal, mass diffusion, and thermoeelastic effects, establishing well-posedness, stability, and providing numerical simulations with error estimates.

Contribution

It introduces a comprehensive analysis of the Bresse-Timoshenko system with thermodiffusion effects, including well-posedness, exponential stability, and numerical schemes with error analysis.

Findings

Proved well-posedness of the system.

Established exponential stability under specific damping conditions.

Developed and validated a finite element numerical scheme.

Abstract

Bresse-Timoshenko beam model with thermal, mass diffusion and theormoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of the solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate for problem under an unusual assumption, and by using a multiplier technique in two different cases, with frictional damping in the angular rotation and with frictional damping in the vertical displacement. In numerical parts, we first obtained a numerical scheme for problem by $P_1$-finite element method for space discretization and implicit Euler scheme for time discretization. Then, we showed that the discrete energy decays, later a priori error estimates are established. Finally , some numerical simulations are presented.