Local Existence and Blow-Up of Solutions for Wave Equation Involving the Fractional Laplacian with Nonlinear Source Term-Reference-Cited by-同舟云学术

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

Published:2023-03-31 Issue:4 Volume:12 Page:343
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Bidi Younes¹²^ORCID,Beniani Abderrahmane³,Bouhali Keltoum⁴⁵,Zennir Khaled⁶^ORCID,ElKhair Hatim M.⁶,Hassan Eltegani I.⁷,Alarfaj Almonther⁷

Affiliation:

1. Laboratoire de Mathématiques Pures et Appliquées (LMPA), Université Amar Telidji de Laghouat, Laghouat 03000, Algeria

2. Ecole Normale Supérieure de Laghouat, Laghouat 03000, Algeria

3. Department of Mathematics, University of Ain Temouchent Belhadj Bouchaib, Ain Temouchent 46000, Algeria

4. Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi Arabia

5. Department of Mathematics, Faculty of Sciences, 20 Aout 1955 University, Skikda 21000, Algeria

6. Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 5701, Riyadh 11432, Saudi Arabia

7. Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia

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.

Funder

Imam Mohammad Ibn Saud Islamic University

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/4/343/pdf

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