Well-posedness and stability for Bresse-Timoshenko type systems with thermodiffusion effects and nonlinear damping

Khaled zennir; Djamel Ouchenane; Abdelbaki Choucha; Mohamad Biomy; Khaled zennir; Djamel Ouchenane; Abdelbaki Choucha; Mohamad Biomy

doi:10.3934/math.2021164

AIMS Mathematics

2021, Volume 6, Issue 3: 2704-2721. doi: 10.3934/math.2021164

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Research article

Well-posedness and stability for Bresse-Timoshenko type systems with thermodiffusion effects and nonlinear damping

1.
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia
2.
Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma. B.P. 401 Guelma 24000, Algérie
3.
Laboratory of pure and applied mathematic, Laghouat University, Algeria
4.
Department of Mathematics, Faculty of Exact Sciences, University of El Oued, B.P. 789, El Oued 39000, Algeria
5.
Department of Mathematics and Computer Science, Faculty of Science, Port Said 42511, University, Egypt

Received: 28 September 2020 Accepted: 13 December 2020 Published: 04 January 2021
MSC : 35BXX, 93B05

Nonlinear 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 solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate under assumption $ (2.3)_{1} $ and polynomial decay rate for solution under $ (2.3)_{2} $, by using a multiplier technique combined with an appropriate Lyapuniv functions.
- Bresse-Timoshenko type systems,
- thermodiffusion effects,
- well-possedness,
- exponential stability,
- polynomial decay,
- nonlinear damping
Citation: Khaled zennir, Djamel Ouchenane, Abdelbaki Choucha, Mohamad Biomy. Well-posedness and stability for Bresse-Timoshenko type systems with thermodiffusion effects and nonlinear damping[J]. AIMS Mathematics, 2021, 6(3): 2704-2721. doi: 10.3934/math.2021164

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Abstract

Nonlinear 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 solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate under assumption $ (2.3)_{1} $ and polynomial decay rate for solution under $ (2.3)_{2} $, by using a multiplier technique combined with an appropriate Lyapuniv functions.

References

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