Exponential stability of a system of coupled wave equations by second order terms with a past history

Zayd Hajjej; Menglan Liao; Zayd Hajjej; Menglan Liao

doi:10.3934/math.20231456

AIMS Mathematics

2023, Volume 8, Issue 12: 28450-28464. doi: 10.3934/math.20231456

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Exponential stability of a system of coupled wave equations by second order terms with a past history

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, Jiangsu 210098, China

Received: 02 September 2023 Revised: 25 September 2023 Accepted: 10 October 2023 Published: 18 October 2023
MSC : 35L05, 93D23, 74D05

In this manuscript we consider a coupled, by second order terms, system of two wave equations with a past history acting on the first equation as a stabilizer. We show that the solution of this system decays exponentially by constructing an appropriate Lyapunov function.
- wave equation,
- exponential stability,
- past history
Citation: Zayd Hajjej, Menglan Liao. Exponential stability of a system of coupled wave equations by second order terms with a past history[J]. AIMS Mathematics, 2023, 8(12): 28450-28464. doi: 10.3934/math.20231456

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Abstract

In this manuscript we consider a coupled, by second order terms, system of two wave equations with a past history acting on the first equation as a stabilizer. We show that the solution of this system decays exponentially by constructing an appropriate Lyapunov function.

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