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Research Article | Open Access

Blow-up dynamics in nonlinear coupled wave equations with fractional damping and external source

Abdelhadi Safsaf1, Suleman Alfalqi2, Ahmed Bchatnia3( ), Abderrahmane Beniani1
Department of Mathematics, University of Ain Temouchent, Faculty of Science and Technology, Engineering and Sustainable Development, Laboratory, Ain Témouchent 46000, Algeria
Department of Mathematics, Applied College in Mahayil, King Khalid University, Abha, Saudi Arabia
LR Analyse Non-Linéaire et Géométrie, LR21ES08, Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia
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Abstract

This study focused on a coupled nonlinear wave equation system featuring fractional damping and polynomial source terms within a bounded domain. We demonstrated that, under specific conditions, the solutions exhibited blow-up in a finite time-frame.

Keywords

wave equationcoupled systemblow-up for solutionCaputo's fractional derivative

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Electronic Research Archive
Volume 32 Issue 10,
October 2024
Pages 5738-5751
DOI: 10.3934/era.2024265

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Cite this article:
Safsaf A, Alfalqi S, Bchatnia A, et al. Blow-up dynamics in nonlinear coupled wave equations with fractional damping and external source. Electronic Research Archive, 2024, 32(10): 5738-5751. https://doi.org/10.3934/era.2024265

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Received: 24 August 2024
Revised: 15 September 2024
Accepted: 27 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 (http://creativecommons.org/licenses/by/4.0)