Global nonexistence for a semilinear Petrovsky equation

被引：70

作者：

Chen, Wenying ^{[2
]}

Zhou, Yong ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[2] Chongqing Three Gorges Univ, Coll Math & Comp Sci, Chongqing 404000, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 09期

关键词：

Blow-up; Semilinear Petrovsky equation; LINEAR EVOLUTION-EQUATIONS; NONLINEAR-WAVE EQUATION; EXISTENCE; THEOREMS; DISSIPATION;

D O I：

10.1016/j.na.2008.04.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a semilinear Petrovsky equation with damping and source terms. It is proved that the solution blows up in Finite time if the positive initial energy satisfies a suitable condition. Moreover for the linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. This is an important breakthrough, since it is only well known that the solution blows up in finite time if the initial energy is negative from all the previous literature. (c) 2008 Elsevier Ltd. All rights reserved.

引用

页码：3203 / 3208

页数：6

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