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Global existence and numerical simulations for a thermoelastic diffusion problem in moving boundary

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  • Madureira, Rodrigo L.R.
  • Rincon, Mauro A.
  • Aouadi, Moncef

Abstract

In this paper we investigate the dynamic behavior and the numerical analysis for a thermoelastic diffusion problem in one space dimension with moving boundary. Global existence is proved by using the penalty method of Lions and the Galerkin approximations. Under suitable conditions, we prove that the energy functional decays to zero as the time tends to infinity by the method of perturbation energy. An uncoupled numerical method was developed to obtain an approximate numerical solution with order of quadratic convergence in time and space. Tables and graphs of the approximate solution are displayed for a copper like material, to verify the efficiency and feasibility of the proposed method. Furthermore, we show that the numerical results are consistent with the theoretical results.

Suggested Citation

  • Madureira, Rodrigo L.R. & Rincon, Mauro A. & Aouadi, Moncef, 2019. "Global existence and numerical simulations for a thermoelastic diffusion problem in moving boundary," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 410-431.
    • Handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:410-431
    DOI: 10.1016/j.matcom.2019.07.001
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    References listed on IDEAS

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    1. Isaías Pereira Jesus, 2016. "Hierarchical Control for the Wave Equation with a Moving Boundary," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 336-350, October.
    2. Luci Harue Fatori & Michelle Klaiber, 2011. "Exponential Decay to Thermoelastic Systems over Noncylindrical Domains," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-10, August.
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    Cited by:

    1. Madureira, Rodrigo L.R. & Rincon, Mauro A. & Aouadi, Moncef, 2021. "Numerical analysis for a thermoelastic diffusion problem in moving boundary," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 630-655.

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