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Research Article | Open Access

Delayed wave equation with logarithmic variable-exponent nonlinearity

Mohammad Kafini1,2( ), Maher Noor2,3
Department of Mathematics, The interdisciplinary research center in construction and building materials
King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Department of Mathematics, Dammam Community College
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Abstract

A delayed nonlinear wave equation with variable exponents of logarithmic type is discussed in this paper. In the presence of the logarithmic nonlinear source, we established a global existence result under sufficient conditions on the initial data only without imposing the Sobolev Logarithmic Inequality. After that, we established global results of exponential and polynomial types according to the range values of the exponents. At the end, we give a numerical study that supports our theoretical results.

Keywords

decaynonlinearly dampeddelay timevariable exponent

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Electronic Research Archive
Volume 31 Issue 5,
May 2023
Pages 2974-2993
DOI: 10.3934/era.2023150

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Cite this article:
Kafini M, Noor M. Delayed wave equation with logarithmic variable-exponent nonlinearity. Electronic Research Archive, 2023, 31(5): 2974-2993. https://doi.org/10.3934/era.2023150

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Received: 11 January 2023
Revised: 01 March 2023
Accepted: 07 March 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)