Global existence and blow-up of solutions for higher-order viscoelastic wave equation with a nonlinear source term

被引：23
作者：
Ye, Yaojun [1 ]
机构：
[1] Zhejiang Univ Sci & Technol, Dept Math & Informat Sci, Hangzhou 310023, Zhejiang, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 112卷
基金：
中国国家自然科学基金;
关键词：
Nonlinear higher-order viscoelastic wave equation; Global existence; Blow-up; Lifespan estimate; Nonlinear source term; HYPERBOLIC-EQUATIONS; DECAY; NONEXISTENCE; ENERGY;
D O I：
10.1016/j.na.2014.09.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The initial-boundary value problem for some nonlinear higher-order viscoelastic wave equation with a nonlinear source term in a bounded domain is studied. The existence of global weak solutions for this problem is established by using the Galerkin method. Meanwhile, under suitable conditions on relaxation function g(center dot) and the positive initial energy as well as non-positive initial energy, it is proved that the solution blows up in the finite time and the lifespan estimates of solutions are also given. (C) 2014 Elsevier Ltd. All rights reserved.
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收藏
页码：129 / 146
页数：18
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