THE INITIAL-BOUNDARY VALUE PROBLEMS FOR A CLASS OF SIXTH ORDER NONLINEAR WAVE EQUATION

被引：40
|
作者：
Xu, Runzhang [1 ,2 ]
Zhang, Mingyou [3 ]
Chen, Shaohua [4 ]
Yang, Yanbing [1 ]
Shen, Jihong [1 ]
机构：
[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Heilongjiang, Peoples R China
[2] Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China
[3] Harbin Engn Univ, Coll Automat, Harbin 150001, Heilongjiang, Peoples R China
[4] Cape Breton Univ, Dept Math, Sydney, NS B1P 6L2, Canada
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 11期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Initial boundary value problem; sixth order wave equation; blow up; existence of global solutions; arbitrarily positive initial energy; SEMILINEAR HYPERBOLIC-EQUATIONS; DOUBLE DISPERSION EQUATIONS; GLOBAL-SOLUTIONS; CAUCHY-PROBLEM; BOUSSINESQ EQUATION; PARABOLIC EQUATIONS; BLOW-UP; NONEXISTENCE; EXISTENCE; INSTABILITY;
D O I：
10.3934/dcds.2017244
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers the initial boundary value problem of solutions for a class of sixth order 1-D nonlinear wave equations. We discuss the probabilities of the existence and nonexistence of global solutions and give some sufficient conditions for the global and non-global existence of solutions at three different initial energy levels, i.e., sub-critical level, critical level and sup-critical level.
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页码：5631 / 5649
页数：19
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