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arXiv · 2011.03680

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

Mohammad Elhindi·Khaled Zennir·Djamel Ouchenane·Abdelbaki Choucha·Toufic El Arwadi
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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.

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Mohammad Elhindi, Khaled Zennir, Djamel Ouchenane, Abdelbaki Choucha, Toufic El Arwadi. 2020-11-07. Bresse-Timoshenko type systems with thermodiffusion effects: Well-possedness, stability and numerical results. https://arxiv.org/abs/2011.03680

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