带势的非线性Klein-Gordon方程柯西问题的稳定和不稳定集(英文)  

Stable and Unstable Sets for the Cauchy Problem for Nonlinear Klein-Gordon Equation with Potential

作　　者：蒋毅[1] 成和平 孟宪良[1] 蒲成林[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066 [2]成教电子机械高等专科学校,成都610031

出　　处：《应用数学》2006年第4期835-841,共7页Mathematica Applicata

摘　　要：对带势的非线性Klein-Gordon方程柯西问题,我们定义了新的对于初值的稳定和不稳定集.我们证明了如果发展进入了不稳定集,解在有限时间内爆破;如果发展进入了稳定集,解整体存在.运用势并讨论,我们回答了当初值为多少时,柯西问题的整体解存在.For the Cauchy problem for the nonlinear Klein-Gordon equation with potential,we define new stable and unstable sets for the initial data. We prove that if during the evolution enters into the unstable set, the solution blows up in finite time. If during the evolution enters into the stable set,the solution is global. By using scaling argument,we also answer the question of how small the initial data are the global solution of the Cauchy problem exists.

关 键 词：KLEIN-GORDON方程 稳定集 不稳定集 整体存在 爆破 

分 类 号：O175.26[理学—数学]