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

Bidi Younes; Abderrahmane Beniani; Khaled Zennir; Zayd Hajjej; Hongwei Zhang; Bidi Younes; Abderrahmane Beniani; Khaled Zennir; Zayd Hajjej; Hongwei Zhang

doi:10.3934/era.2024243

Electronic Research Archive

2024, Volume 32, Issue 9: 5268-5286. doi: 10.3934/era.2024243

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

1.
Department of Mathematics, College of Science, University of Djillali Liabes - B. P. 89, Sidi Bel Abbes 22000, Algeria
2.
Ecole Normale Supérieure de Laghouat, Laboratoire des Mathématiques Pures et Appliquées
3.
Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, , University of Ain Temouchent, Ain Temouchent, 46000, Algeria
4.
Department of Mathematics, Faculty of Sciences, University 20 Août 1955- Skikda, Algeria
5.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
6.
Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China

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

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.
- fractional Laplacian,
- differential equations,
- global existence,
- partial differential equations,
- logarithmic nonlinearity,
- Galerkin approximations
Citation: Bidi Younes, Abderrahmane Beniani, Khaled Zennir, Zayd Hajjej, Hongwei Zhang. Global solution for wave equation involving the fractional Laplacian with logarithmic nonlinearity[J]. Electronic Research Archive, 2024, 32(9): 5268-5286. doi: 10.3934/era.2024243

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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.

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