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.

引用

页码：1408 / 1425

页数：18

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