Exponential decay in a delayed wave equation with variable coefficients

Waled Al-Khulaifi; Manal Alotibi; Nasser-Eddine Tatar; Waled Al-Khulaifi; Manal Alotibi; Nasser-Eddine Tatar

doi:10.3934/math.20241348

AIMS Mathematics

2024, Volume 9, Issue 10: 27770-27783. doi: 10.3934/math.20241348

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Research article

Exponential decay in a delayed wave equation with variable coefficients

1.
King Fahd University of Petroleum & Minerals, Department of Mathematics, Dhahran, 31261, Saudi Arabia
2.
Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, 31261, Saudi Arabia
3.
Center for Integrative Petroleum Research, KFUPM, Dhahran, 31261, Saudi Arabia
4.
Interdisciplinary Research Center for Intelligent Manufacturing and Robotics, KFUPM, Dhahran, 31261, Saudi Arabia

Received: 20 July 2024 Revised: 09 September 2024 Accepted: 21 September 2024 Published: 26 September 2024
MSC : 35B40, 35L05, 35L20, 93D23

We establish an exponential stability result for a wave equation that includes weighted coefficients of structural damping and a delayed term. This study reveals cases where the delayed term may not be dominated by the damping term, yet the system is exponentially stable. Our coefficients do not obey necessarily the conditions that are usually imposed in the literature.
- wave equation,
- energy decay,
- time delay,
- strong damping,
- exponential stability
Citation: Waled Al-Khulaifi, Manal Alotibi, Nasser-Eddine Tatar. Exponential decay in a delayed wave equation with variable coefficients[J]. AIMS Mathematics, 2024, 9(10): 27770-27783. doi: 10.3934/math.20241348

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Abstract

We establish an exponential stability result for a wave equation that includes weighted coefficients of structural damping and a delayed term. This study reveals cases where the delayed term may not be dominated by the damping term, yet the system is exponentially stable. Our coefficients do not obey necessarily the conditions that are usually imposed in the literature.

References

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