Global existence and blowup of solutions for a class of nonlinear higher-order wave equations

被引：7

作者：

Zhou, Jun ^{[1
]}

Wang, Xiongrui ^{[2
]}

Song, Xiaojun ^{[3
]}

Mu, Chunlai ^{[4
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] Yibin Coll, Dept Math, Yibin 644007, Peoples R China

[3] China W Normal Univ, Dept Math, Nanchong 637002, Peoples R China

[4] Chongqing Univ, Sch Math & Stat, Chongqing 400044, Peoples R China

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2012年 / 63卷 / 03期

关键词：

Global existence; Blowup; Energy decay; Lifespan; ENERGY DECAY; NONEXISTENCE;

D O I：

10.1007/s00033-011-0165-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a class of nonlinear higher-order wave equation with nonlinear damping u(tt) + (-Delta)(m)u+a vertical bar u(t)vertical bar(p-2)(ut) = b vertical bar u vertical bar(q-2)(u) in a bounded domain Omega subset of R-N (N >= 1 is a natural number). We show that the solution is global in time under some conditions without the relation between p and q and we also show that the local solution blows up in finite time if q > p with some assumptions on initial energy. The decay estimate of the energy function for the global solution and the lifespan for the blow-up solution are given. This extend the recent results of Ye (J Ineq Appl, 2010).

引用

页码：461 / 473

页数：13

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