Exploring Thermoelastic Effects in Damped Bresse Systems with Distributed Delay

Abdelbaki Choucha, Djamel Ouchenane, Safa M. Mirgani, Eltigan I. Hassan, A. H. A. Alfedeel and Khaled Zennir ()
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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

Mathematics, 2024, vol. 12, issue 6, 1-19

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.

Keywords: Lyapunov functions; distributed delay; Bresse system; general decay; thermoelasticity; second sound; relaxation function; partial differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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