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

2020/11/07 by Elhindi, Mohammad, Zennir, Khaled, Ouchenane, Djamel +2
#Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2011.03680

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 P₁-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.

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