On a class of a coupled nonlinear viscoelastic Kirchhoff equations variable-exponents: global existence, blow up, growth and decay of solutions

被引：1

作者：

Choucha, Abdelbaki ^{[1
,2
]}

Haiour, Mohamed ^{[3
]}

Boulaaras, Salah ^{[4
]}

机构：

[1] Amar Teleji Laghouat Univ, Fac Sci, Dept Mat Sci, Laghouat, Algeria

[2] Ghardaia Univ, Lab Math & Appl Sci, Ghardaia, Algeria

[3] Badji Mokhtar Annaba Univ, Fac Sci, Dept Math, POB 12, Annaba 23000, Algeria

[4] Qassim Univ, Coll Sci, Dept Math, Buraydah 51452, Saudi Arabia

来源：

BOUNDARY VALUE PROBLEMS | 2024年 / 2024卷 / 01期

关键词：

Viscoelastic equation; Global existence; Blow up; Exponential growth; General decay; Variable exponents; NONEXISTENCE THEOREMS; WAVE EQUATIONS;

D O I：

10.1186/s13661-024-01864-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term.

引用

页数：30

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