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

Abdelhadi Safsaf; Suleman Alfalqi; Ahmed Bchatnia; Abderrahmane Beniani; Abdelhadi Safsaf; Suleman Alfalqi; Ahmed Bchatnia; Abderrahmane Beniani

doi:10.3934/era.2024265

Electronic Research Archive

2024, Volume 32, Issue 10: 5738-5751. doi: 10.3934/era.2024265

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Research article

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

1.
Department of Mathematics, University of Ain Temouchent, Faculty of Science and Technology, Engineering and Sustainable Development, Laboratory, Ain Témouchent 46000, Algeria
2.
Department of Mathematics, Applied College in Mahayil, King Khalid University, Abha, Saudi Arabia
3.
LR Analyse Non-Linéaire et Géométrie, LR21ES08, Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia

Received: 24 August 2024 Revised: 15 September 2024 Accepted: 27 September 2024 Published: 21 October 2024

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.
- wave equation,
- coupled system,
- blow-up for solution,
- Caputo's fractional derivative
Citation: Abdelhadi Safsaf, Suleman Alfalqi, Ahmed Bchatnia, Abderrahmane Beniani. Blow-up dynamics in nonlinear coupled wave equations with fractional damping and external source[J]. Electronic Research Archive, 2024, 32(10): 5738-5751. doi: 10.3934/era.2024265

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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.

References

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