Energy decay of solution for nonlinear delayed transmission problem

Abdelkader Moumen; Abderrahmane Beniani; Tariq Alraqad; Hicham Saber; Ekram. E. Ali; Keltoum Bouhali; Khaled Zennir; Abdelkader Moumen; Abderrahmane Beniani; Tariq Alraqad; Hicham Saber; Ekram. E. Ali; Keltoum Bouhali; Khaled Zennir

doi:10.3934/math.2023707

AIMS Mathematics

2023, Volume 8, Issue 6: 13815-13829. doi: 10.3934/math.2023707

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Energy decay of solution for nonlinear delayed transmission problem

1.
Department of Mathematics, Faculty of Sciences, University of Ha'il, Ha'il 55425, Saudi Arabia
2.
Laboratory ACEDP, Center University of Belhadj Bouchaib, Ain Temouchent 46000, Algeria
3.
Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass, Saudi Arabia
4.
Departement de Mathématiques, Faculté des sciences, Université 20 A\^out 1955, Skikda, Algérie
5.
Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945- Guelma, Guelma 24000, Algeria

Received: 03 October 2022 Revised: 12 March 2023 Accepted: 20 March 2023 Published: 12 April 2023
MSC : 35B37, 35L55, 74D05, 93D15, 93D20

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.
- nonlinear transmission problem,
- delay term,
- decay rate,
- Lyapunov functions
Citation: Abdelkader Moumen, Abderrahmane Beniani, Tariq Alraqad, Hicham Saber, Ekram. E. Ali, Keltoum Bouhali, Khaled Zennir. Energy decay of solution for nonlinear delayed transmission problem[J]. AIMS Mathematics, 2023, 8(6): 13815-13829. doi: 10.3934/math.2023707

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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.

References

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