General stability for a system of coupled quasi-linear and linear wave equations and with memory term

Zayd Hajjej; Menglan Liao; Zayd Hajjej; Menglan Liao

doi:10.3934/math.20231567

AIMS Mathematics

2023, Volume 8, Issue 12: 30668-30682. doi: 10.3934/math.20231567

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General stability for a system of coupled quasi-linear and linear wave equations and with memory term

Zayd Hajjej ^{1
,
,},
Menglan Liao ²

1.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2.
School of Mathematics, Hohai University, Nanjing, 210098 Jiangsu, China

Received: 12 September 2023 Revised: 05 November 2023 Accepted: 08 November 2023 Published: 13 November 2023
MSC : 35B35, 35B40, 93D23

In this paper, a system of coupled quasi-linear and linear wave equations with a finite memory term is concerned. By constructing an appropriate Lyapunov function, we prove that the total energy associated with the system is stable under suitable conditions on memory kernel.
- coupled wave equations,
- finite memory,
- exponential stability,
- nonlinearity
Citation: Zayd Hajjej, Menglan Liao. General stability for a system of coupled quasi-linear and linear wave equations and with memory term[J]. AIMS Mathematics, 2023, 8(12): 30668-30682. doi: 10.3934/math.20231567

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Abstract

In this paper, a system of coupled quasi-linear and linear wave equations with a finite memory term is concerned. By constructing an appropriate Lyapunov function, we prove that the total energy associated with the system is stable under suitable conditions on memory kernel.

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