带竞争势的非线性Klein-Gordon方程的稳定集和不稳定集  

Stable and Unstable Sets of the Nonlinear Klein-Gordon Equation with Competing Potentials

作　　者：蒋毅[1] 甘在会[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610068

出　　处：《应用数学学报》2008年第4期744-751,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10771151;10726034;10801102);四川省青年科技基金(07ZQ026-009).

摘　　要：本文研究带竞争势的非线性Klein-Gordon方程的柯西问题.首先定义了新的稳定集和不稳定集.其次证明了如果初值进入不稳定集,该柯西问题的解在有限时间内爆破;如果初值进入稳定集,该柯西问题的整体解存在.最后运用势井讨论,我们回答了当初值在什么范围时,该柯西问题的整体解存在这个问题.This paper deals with the Cauchy problem for the nonlinear Klein-Gordon equation with competing potentials. Firstly, we define new stable and unstable sets. Then we prove that if the initial data enter into the unstable set, then the solution of the aforementioned Cauchy problem blows up in finite time, and if the initial data enter into the stable set, then the solution of the aforementioned Cauchy problem globally exists. Finally, by using scaling argument, we answer the question： which domain are the initial data in, the global solution to the Cauchy problem exists.

关 键 词：非线性KLEIN-GORDON方程 竞争势 稳定集 不稳定集 整体解 爆破 

分 类 号：O175.27[理学—数学]