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

共 50 条

[41] Strongly nonlinear variational parabolic initial-boundary value problems
Akdim, Youssef
Benkirane, Abdelmoujib
El Moumni, Mostafa
Fri, Aziz
ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2014, 41 (02): : 177 - 189
[42] On the order of accuracy for difference approximations of initial-boundary value problems
Svard, Magnus
Nordstrom, Jan
JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 218 (01) : 333 - 352
[43] Initial-boundary value problems for nonlinear systems of conservation laws
D. Amadori
Nonlinear Differential Equations and Applications NoDEA, 1997, 4 : 1 - 42
[44] Initial-boundary value problems for nonlinear systems of conservation laws
Amadori, Debora
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 1997, 4 (01): : 1 - 42
[45] A BGK approximation to nonlinear parabolic initial-boundary value problems
Guarguaglini, FR
Terracina, A
ASYMPTOTIC ANALYSIS, 2001, 28 (01) : 75 - 89
[46] Initial Boundary Value Problems for a Class of N-Dimensional Nonlinear Wave Systems of Fourth Order
Ding, L. J.
Xiao, L. M.
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2014, 38 (06) : 791 - 802
[47] Initial-Boundary Value Problem for a Third-Order Semilinear Hyperbolic Equation with the Wave Operator
V. I. Korzyuk
J. V. Rudzko
Lobachevskii Journal of Mathematics, 2024, 45 (11) : 5569 - 5580
[48] On the solvability of nonlocal initial-boundary value problems for a partial differential equation of high even order
Urinov, A. K.
Azizov, M. S.
VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI, 2022, 32 (02): : 240 - 255
[49] An initial-boundary value problem for a nonlinear wave equation in an n-dimensional rectangular domain
Vagabov, AI
DIFFERENTIAL EQUATIONS, 2000, 36 (10) : 1484 - 1492
[50] An initial-boundary value problem for a nonlinear wave equation in ann-dimensional rectangular domain
A. I. Vagabov
Differential Equations, 2000, 36 : 1484 - 1492

← 1 2 3 4 5 →