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Research Article | Open Access

Global solution for wave equation involving the fractional Laplacian with logarithmic nonlinearity

Bidi Younes1,2, Abderrahmane Beniani3, Khaled Zennir4( ), Zayd Hajjej5, Hongwei Zhang6
Department of Mathematics, College of Science, University of Djillali Liabes - B. P. 89, Sidi Bel Abbes 22000, Algeria
Ecole Normale Supérieure de Laghouat, Laboratoire des Mathématiques Pures et Appliquées
Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, , University of Ain Temouchent, Ain Temouchent, 46000, Algeria
Department of Mathematics, Faculty of Sciences, University 20 Août 1955- Skikda, Algeria
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China
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Abstract

We construct the global existence for a wave equation involving the fractional Laplacian with a logarithmic nonlinear source by using the Galerkin approximations. The corresponding results for equations with classical Laplacian are considered as particular cases of our assertions.

Keywords

fractional Laplaciandifferential equationsglobal existencepartial differential equationslogarithmic nonlinearityGalerkin approximations

References

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Electronic Research Archive
Volume 32 Issue 9,
September 2024
Pages 5268-5286
DOI: 10.3934/era.2024243

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Cite this article:
Younes B, Beniani A, Zennir K, et al. Global solution for wave equation involving the fractional Laplacian with logarithmic nonlinearity. Electronic Research Archive, 2024, 32(9): 5268-5286. https://doi.org/10.3934/era.2024243

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Received: 29 May 2024
Revised: 26 August 2024
Accepted: 05 September 2024
Published: 12 September 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)