Initial boundary value problem for a class of fourth-order wave equation with viscous damping term

被引：17

作者：

Xu, Runzhang ^{[1
]}

Wang, Shuo ^{[2
]}

Yang, Yanbing ^{[1
]}

Ding, Yunhua ^{[1
]}

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：

APPLICABLE ANALYSIS | 2013年 / 92卷 / 07期

基金：

中国国家自然科学基金;

关键词：

fourth-order nonlinear wave equation; viscous damping; global existence; nonexistence; potential well; DOUBLE DISPERSION EQUATIONS; KLEIN-GORDON EQUATIONS; SEMILINEAR HYPERBOLIC-EQUATIONS; GLOBAL NONEXISTENCE THEOREMS; CAUCHY-PROBLEM; NONLINEAR SCHRODINGER; EVOLUTION-EQUATIONS; BLOW-UP; BOUSSINESQ EQUATION; PARABOLIC EQUATIONS;

D O I：

10.1080/00036811.2012.682058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study the initial boundary value problem for a class of fourth-order nonlinear wave equation with viscous damping term u(tt)-u(xxt)+u(xxxx)=f(u(x))(x). By argument related to the potential well-convexity method, we prove the global existence and nonexistence of the solution. Further, we give some sharp conditions for global existence and nonexistence of the solution. This generalizes the results obtained in Chen and Lu [G. Chen and B. Lu, The initial-boundary value problems for a class of nonlinear wave equations with damping term, J. Math. Anal. Appl. 351 (2009), pp. 1-15].

引用

页码：1403 / 1416

页数：14

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