Global and blow-up solutions for a quasilinear hyperbolic equation with strong damping

被引：2
|
作者：
Sun, Fuqin [1 ]
Wang, Mingxin [2 ]
Li, Huiling [2 ]
机构：
[1] Tianjin Univ Technol & Educ, Sch Sci, Tianjin 300222, Peoples R China
[2] Southeast Univ, Dept Math, Nanjing 210096, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Hyperbolic equation; Strong damping; Global solutions; Blow-up; Decay estimates; NONLINEAR-WAVE EQUATION; EXISTENCE UNIQUENESS; ASYMPTOTIC-BEHAVIOR; EVOLUTION-EQUATIONS; STABILITY; VISCOELASTICITY;
D O I：
10.1016/j.na.2010.05.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study a quasilinear hyperbolic equation with strong damping. Firstly, by use of the successive approximation method and a series of classical estimates, we prove the local existence and uniqueness of a weak solution. Secondly, via some inequalities, the potential method and the concave method, we derive the asymptotic and blow-up behavior of the weak solution with different conditions. (C) 2010 Elsevier Ltd. All rights reserved.
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页码：1408 / 1425
页数：18
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