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.

引用

页码：5631 / 5649

页数：19

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