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Numerical exponential decay of thermoelastic waves connected in parallel

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Abstract

In this paper, we study a system consisting of two wave equations connected in parallel and coupled to the heat diffusion equation. In the first moment, we present theoretical results on existence and uniqueness of solution and we prove the exponential stabilization of the associated semigroup. We analyze the semi-discrete problem in finite differences and we introduce for the first time in the literature the energy method to prove the exponential stabilization of the corresponding semi-discrete system. Finally, we present a fully discrete finite difference scheme that combines explicit and implicit integration methods and numerical simulations that illustrate the theoretical results.

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Acknowledgements

We would like to thank the anonymous referees for carefully reading our manuscript and for giving constructive comments which improved the quality of this paper.

Funding

A. J. A. Ramos was partially supported by CNPq Grant 310729/2019-0. D. S. Almeida Júnior was partially supported by CNPq Grant 314273/2020-4. M. M. Freitas was partially supported by CNPq Grant 313081/2021-2. R. C. Barbosa thanks CAPES (Brazil) for funding the doctoral scholarship.

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Authors and Affiliations

  1. Faculty of Mathematics, Federal University of Pará, Raimundo Santana Street s/n, Salinópolis, 68721-000, PA, Brazil

    A. J. A. Ramos & M. M. Freitas

  2. Program in Mathematics, Federal University of Pará, Augusto Corrêa Street 01, Belém, 66075-110, PA, Brazil

    A. D. S. Campelo, D. S. Almeida Júnior & R. C. Barbosa

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  1. A. J. A. Ramos
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  2. A. D. S. Campelo
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  3. D. S. Almeida Júnior
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Correspondence to A. J. A. Ramos.

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Communicated by Stéphanie Chaillat.

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Ramos, A.J.A., Campelo, A.D.S., Almeida Júnior, D.S. et al. Numerical exponential decay of thermoelastic waves connected in parallel. Adv Comput Math 49, 29 (2023). https://doi.org/10.1007/s10444-023-10027-1

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