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耦合非线性Klein-Gordon方程组的整体解
引用本文:甘在会,张健.耦合非线性Klein-Gordon方程组的整体解[J].应用数学和力学,2007,28(5):603-613.
作者姓名:甘在会  张健
作者单位:四川师范大学,数学与软件科学学院,成都,610068
基金项目:国家自然科学基金;四川省青年科技基金
摘    要:研究二维空间中一类耦合非线性Klein-Gordon方程组的整体解.首先,通过构造交叉强制变分问题且建立发展流的交叉不变流形,得到了该方程组解爆破和整体存在的一个最佳条件.然后利用尺度变换讨论证明了当初值为多小时,该方程组的整体解存在.

关 键 词:耦合非线性Klein-Gordon方程组  整体解  爆破  交叉强制变分问题  最佳条件
文章编号:1000-0887(2007)05-0603-11
修稿时间:2006-04-04

Global Solution for a Coupled Nonlinear Klein-Gordon System
GAN Zai-hui,ZHANG Jian.Global Solution for a Coupled Nonlinear Klein-Gordon System[J].Applied Mathematics and Mechanics,2007,28(5):603-613.
Authors:GAN Zai-hui  ZHANG Jian
Institution:College of Mathematics and Software Science; Sichuan Normal University; Chengdu 610068; P.R.China
Abstract:The global solution for a coupled nonlinear Klein-Gordon system in two space dimensions is studied.First,a sharp threshold of blowup and global existence for the system is obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data are for which the solution of the system exists globally is proved by using the scaling argument.
Keywords:couple nonlinear Klein-Gordon system  Global solution  blow up  cross-constrained variational problem  sharp threshold
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