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Research Article | Open Access

Exponential decay in a delayed wave equation with variable coefficients

Waled Al-Khulaifi1,2( ), Manal Alotibi1,3, Nasser-Eddine Tatar1,4
King Fahd University of Petroleum & Minerals, Department of Mathematics, Dhahran, 31261, Saudi Arabia
Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, 31261, Saudi Arabia
Center for Integrative Petroleum Research, KFUPM, Dhahran, 31261, Saudi Arabia
Interdisciplinary Research Center for Intelligent Manufacturing and Robotics, KFUPM, Dhahran, 31261, Saudi Arabia
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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.

Keywords

wave equationenergy decaytime delaystrong dampingexponential stability
CLC number: 35B40, 35L05, 35L20, 93D23

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 27770-27783
DOI: 10.3934/math.20241348

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Cite this article:
Al-Khulaifi W, Alotibi M, Tatar N-E. Exponential decay in a delayed wave equation with variable coefficients. AIMS Mathematics, 2024, 9(10): 27770-27783. https://doi.org/10.3934/math.20241348

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Received: 20 July 2024
Revised: 09 September 2024
Accepted: 21 September 2024
Published: 15 October 2024
©2024 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)