Global existence, asymptotic behavior and blow-up of solutions for a suspension bridge equation with nonlinear damping and source terms

被引：18

作者：

Liu, Wenjun ^{[1
]}

Zhuang, Hefeng ^{[1
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Coll Math & Stat, Nanjing 210044, Jiangsu, Peoples R China

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2017年 / 24卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Suspension bridges; Fourth order wave equation; Nonlinear damping; Source term; Existence; Blow up; WAVE-EQUATIONS; ENERGY DECAY; RECTANGULAR PLATE; NONEXISTENCE; OSCILLATIONS; ATTRACTOR; INSTABILITY; STABILITY; BOUNDARY; SYSTEM;

D O I：

10.1007/s00030-017-0491-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term vertical bar u(t)vertical bar(m-2) u(t) and source term vertical bar u vertical bar(p-2) u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p > m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T-max is also established. It worth to mention that our obtained results extend the recent results of Wang (J Math Anal Appl 418(2): 713-733, 2014) to the nonlinear damping case.

引用

页数：35

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