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

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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 with frictional damping in the vertical displacement. Numerically, we construct a numerical scheme based on the \(P_1\)-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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Acknowledgements

For any decision, the authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, Lebanon

    M. Elhindi & T. El Arwadi

  2. Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia

    Kh. Zennir

  3. Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma, B.P. 401, 24000, Guelma, Algeria

    Kh. Zennir

  4. Laboratory of Pure and Applied Mathematic, Laghouat University, Laghouat, Algeria

    D. Ouchenane

  5. Department of Mathematics, Faculty of Exact Sciences, University of El Oued, B.P. 789, 39000, El Oued, Algeria

    A. Choucha

Authors
  1. M. Elhindi
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  2. Kh. Zennir
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  3. D. Ouchenane
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  4. A. Choucha
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  5. T. El Arwadi
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Correspondence to T. El Arwadi.

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Elhindi, M., Zennir, K., Ouchenane, D. et al. Bresse-Timoshenko type systems with thermodiffusion effects: well-possedness, stability and numerical results. Rend. Circ. Mat. Palermo, II. Ser 72, 169–194 (2023). https://doi.org/10.1007/s12215-021-00672-0

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  • DOI: https://doi.org/10.1007/s12215-021-00672-0

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