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

被引：1

作者：

Bidi, Younes ^{[1
,2
]}

Beniani, Abderrahmane ^{[3
]}

Bouhali, Keltoum ^{[4
,5
]}

Zennir, Khaled ^{[6
]}

ElKhair, Hatim M. ^{[6
]}

Hassan, Eltegani I. ^{[7
]}

Alarfaj, Almonther ^{[7
]}

机构：

[1] Univ Amar Telidji Laghouat, Lab Math Pures & Appl LMPA, Laghouat 03000, Algeria

[2] Ecole Normale Super Laghouat, Laghouat 03000, Algeria

[3] Univ Ain Temouchent Belhadj Bouchaib, Dept Math, Ain Temouchent 46000, Algeria

[4] Qassim Univ, Coll Sci & Arts, Dept Math, Ar Rass 51452, Saudi Arabia

[5] 20 Aout 1955 Univ, Fac Sci, Dept Math, Skikda 21000, Algeria

[6] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Deanship Sci Res, POB 5701, Riyadh 11432, Saudi Arabia

[7] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Dept Math & Stat, Riyadh 11432, Saudi Arabia

来源：

AXIOMS | 2023年 / 12卷 / 04期

关键词：

fractional derivatives; existence; fractional Laplacian; local solution; blow-up; GLOBAL EXISTENCE; SOBOLEV SPACES; SYSTEM;

D O I：

10.3390/axioms12040343

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：19

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