Local Existence and Blow-Up of Solutions for Wave Equation Involving the Fractional Laplacian with Nonlinear Source Term

Younes Bidi,Keltoum Bouhali,Almonther Alarfaj,Khaled Zennir,Abderrahmane Beniani,Hatim M Elkhair,Eltegani I Hassan

doi:10.3390/axioms12040343

Local Existence and Blow-Up of Solutions for Wave Equation Involving the Fractional Laplacian with Nonlinear Source Term

Younes Bidi, Keltoum Bouhali + Show 5 more

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https://doi.org/10.3390/axioms12040343

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Journal: Axioms	Publication Date: Mar 31, 2023
Citations: 1	License type: CC BY 4.0

Affiliation: University of Laghouat, Qassim University, University of Skikda, Imam Mohammad ibn Saud Islamic University, Université de ain Témouchent

#Local Existence #Nonlinear Source Term + Show 8 more

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Abstract

The aim of this paper is to investigate the local weak existence and vacuum isolating of solutions, asymptotic behavior, and blow-up of the solutions for a wave equation involving the fractional Laplacian with nonlinear source. By means of the Galerkin approximations, we prove the local weak existence and finite time blow-up of the solutions and we give the upper and lower bounds for blow-up time.

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