Global Existence, Blow-up and Asymptotic Behavior of Solutions for a Class of Coupled Nonlinear Klein-Gordon Equations with Damping Terms

被引：6

作者：

Wu, Shun-Tang ^{[1
]}

机构：

[1] Natl Taipei Univ Technol, Gen Educ Ctr, Taipei 106, Taiwan

来源：

ACTA APPLICANDAE MATHEMATICAE | 2012年 / 119卷 / 01期

关键词：

Klein-Gordon equations; Damping terms; Potential well; Blow-up; Asymptotic behavior; SEMILINEAR WAVE-EQUATIONS; STANDING WAVES; SCHRODINGER SYSTEM; STRONG INSTABILITY; CAUCHY-PROBLEM; NONEXISTENCE;

D O I：

10.1007/s10440-011-9662-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article studies the Cauchy problem for the coupled nonlinear Klein-Gordon equations with damping terms. By introducing a family of potential wells, we derive the invariant sets and the vacuum isolating of solutions. Furthermore, we show the global existence, finite time blow-up, as well as the asymptotic behavior of solutions. In particular, we establish a sharp criterion for global existence and blow-up of solutions when E(0)< d. Finally, a blow-up result of solutions with E(0)=d is also proved.

引用

页码：75 / 95

页数：21

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