Potential well method for Cauchy problem of generalized double dispersion equations

被引：50
作者：
Liu Yacheng [1 ]
Xu Runzhang [1 ,2 ]
机构：
[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Peoples R China
[2] Harbin Engn Univ, Coll Automat, Harbin 150001, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 338卷 / 02期
基金：
中国国家自然科学基金;
关键词：
generalized double dispersion equations; Cauchy problem; potential wells; global existence; nonexistence; NONLINEAR-WAVE EQUATIONS; GLOBAL EXISTENCE; ASYMPTOTIC STABILITY; BLOW-UP; INSTABILITY;
D O I：
10.1016/j.jmaa.2007.05.076
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study Cauchy problem of generalized double dispersion equations u(tt)-u(xx)-u(xxtt)+u(xxxx)=f(u)(xx), where f (u) = |u|(p), p > 1 or u(2k), k = 1, 2,.... By introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions, but also obtain the invariance of some sets and vacuum isolating of solutions. In addition, the global existence and finite time blow up of solutions for problem with critical initial conditions E (0) = d, I (u(0)) >= 0 or I (u(0)) < 0 are proved. (C) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：1169 / 1187
页数：19
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