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
收藏
页码：717 / 737
页数：21
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