| 带势的非线性Klein-Gordon方程柯西问题的稳定和不稳定集 |
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| 引用本文： | 蒋毅,成和平,孟宪良,蒲成林.带势的非线性Klein-Gordon方程柯西问题的稳定和不稳定集[J].应用数学,2006,19(4):835-841. |
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| 作者姓名： | 蒋毅 成和平 孟宪良 蒲成林 |
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| 作者单位： | 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 |
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| 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.
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| 关 键 词： | Klein-Gordon方程 稳定集 不稳定集 整体存在 爆破 |
| 文章编号： | 1001-9847(2006)04-0835-07 |
| 收稿时间： | 2005-04-13 |
| 修稿时间： | 2005年4月13日 |
Stable and Unstable Sets for the Cauchy Problem for Nonlinear Klein-Gordon Equation with Potential |
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| JIANG Yi,CHENG He-ping,MENG Xian-lian,PU Zhi-lin.Stable and Unstable Sets for the Cauchy Problem for Nonlinear Klein-Gordon Equation with Potential[J].Mathematica Applicata,2006,19(4):835-841. |
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| Authors: | JIANG Yi CHENG He-ping MENG Xian-lian PU Zhi-lin |
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| Institution: | 1. College of Mathematics and Software Science, Sichuna Normal University, Chengdu 610066 ,China ;2. Chengdu Electromechanical College ,Chengdu 610031 ,China |
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| Abstract: | 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. |
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| Keywords: | Klein-Gordon equation Stable set Unstable set Global existence Blowup |
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