Existence and blow up for viscoelastic hyperbolic equations with variable exponents

被引：1

作者：

Chu, Ying ^{[1
]}

Wen, Bo ^{[1
]}

Cheng, Libo ^{[1
]}

机构：

[1] Changchun Univ Sci & Technol, Sch Math & Stat, Changchun 130022, Peoples R China

来源：

COMMUNICATIONS IN ANALYSIS AND MECHANICS | 2024年 / 16卷 / 04期

关键词：

variable exponents; weak solutions; viscoelastic; existence; blow up; INITIAL-ENERGY SOLUTIONS; WAVE-EQUATION;

D O I：

10.3934/cam.2024032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider a nonlinear viscoelastic hyperbolic problem with variable exponents. By using the Faedo-Galerkin method and the contraction mapping principle, we obtain the existence of weak solutions under suitable assumptions on the variable exponents m ( x ) and p ( x ). Then we prove that a solution blows up in finite time with positive initial energy as well as nonpositive initial energy.

引用

页码：717 / 737

页数：21

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