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Research Article | Open Access

Decay result in a problem of a nonlinearly damped wave equation with variable exponent

Mohammad Kafini1,3( ), Jamilu Hashim Hassan1, Mohammad M. Al-Gharabli2,3
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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Abstract

In this work we study a wave equation with a nonlinear time dependent frictional damping of variable exponent type. The existence and uniqueness results are established using Fadeo-Galerkin approximation method. We also exploit the Komornik lemma to prove the uniform stability result for the energy associated to the solution of the problem under consideration.

Keywords

viscoelasticityrelaxation functiongeneral decaylogarithmic nonlinearityvariable exponent
CLC number: 35B37, 35L55, 74D05, 93D15, 93D20

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 3067-3082
DOI: 10.3934/math.2022170

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Kafini M, Hassan JH, Al-Gharabli MM. Decay result in a problem of a nonlinearly damped wave equation with variable exponent. AIMS Mathematics, 2022, 7(2): 3067-3082. https://doi.org/10.3934/math.2022170

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Received: 19 August 2021
Accepted: 19 November 2021
Published: 15 February 2022
©2022 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)