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Exploring Thermoelastic Effects in Damped Bresse Systems with Distributed Delay

Author

Listed:
  • Abdelbaki Choucha

    (Department of Mathematics, Faculty of Exact Sciences, University of El Oued, El Oued 39000, Algeria)

  • Djamel Ouchenane

    (Laboratory of Pure and Applied Mathematic, University of Laghouat, Laghouat 03000, Algeria)

  • Safa M. Mirgani

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Eltigan I. Hassan

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • A. H. A. Alfedeel

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Khaled Zennir

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, University of 20 Août 1955, Skikda 21000, Algeria)

Abstract

In this work, we consider the one-dimensional thermoelastic Bresse system by addressing the aspects of nonlinear damping and distributed delay term acting on the first and the second equations. We prove a stability result without the common assumption regarding wave speeds under Neumann boundary conditions. We discover a new relationship between the decay rate of the solution and the growth of ϖ at infinity. Our results were achieved using the multiplier method and the perturbed modified energy, named Lyapunov functions together with some properties of convex functions.

Suggested Citation

  • Abdelbaki Choucha & Djamel Ouchenane & Safa M. Mirgani & Eltigan I. Hassan & A. H. A. Alfedeel & Khaled Zennir, 2024. "Exploring Thermoelastic Effects in Damped Bresse Systems with Distributed Delay," Mathematics, MDPI, vol. 12(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:857-:d:1357299
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