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Research Article | Open Access

Energy decay of solution for nonlinear delayed transmission problem

Abdelkader Moumen1, Abderrahmane Beniani2, Tariq Alraqad1, Hicham Saber1, Ekram. E. Ali1, Keltoum Bouhali3,4, Khaled Zennir3,5( )
Department of Mathematics, Faculty of Sciences, University of Ha'il, Ha'il 55425, Saudi Arabia
Laboratory ACEDP, Center University of Belhadj Bouchaib, Ain Temouchent 46000, Algeria
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia
Departement de Mathématiques, Faculté des sciences, Université 20 A\^out 1955, Skikda, Algérie
Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945- Guelma, Guelma 24000, Algeria
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Abstract

In this work, we consider a nonlinear transmission problem in the bounded domain with a delay term in the first equation. Under conditions on the weight of the damping and the weight of the delay, we prove general stability estimates by introducing a suitable Lyapunov functional and using the properties of convex functions.

Keywords

nonlinear transmission problemdelay termdecay rateLyapunov functions
CLC number: 35B37, 35L55, 74D05, 93D15, 93D20

References

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 13815-13829
DOI: 10.3934/math.2023707

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Cite this article:
Moumen A, Beniani A, Alraqad T, et al. Energy decay of solution for nonlinear delayed transmission problem. AIMS Mathematics, 2023, 8(6): 13815-13829. https://doi.org/10.3934/math.2023707

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Received: 03 October 2022
Revised: 12 March 2023
Accepted: 20 March 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)