| 非线性Klein-Gordon方程整体解存在的最佳条件 |
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| 引用本文： | 甘在会,张健. 非线性Klein-Gordon方程整体解存在的最佳条件[J]. 数学学报, 2005, 48(2): 311-318. DOI: cnki:ISSN:0583-1431.0.2005-02-013 |
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| 作者姓名： | 甘在会 张健 |
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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／／四川大学数学学院,成都610064 [2]四川师范大学数学与软件科学学院,成都610066 |
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| 基金项目： | 国家自然科学基金资助项目(10271084) |
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| 摘 要： | 本文研究一类带竞争势函数的非线性Klein-Gordon方程的柯西问题.根据基 态的特征,运用势井方法和凹方法导出了该问题解爆破和整体存在的最佳条件. 同时 还回答了当初值为多小时,整体解存在这个问题.
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| 关 键 词： | 非线性Klein-Gordon方程 最佳条件 整体解 |
Sharp Conditions of Global Existence for Nonlinear Klein-Gordon Equations |
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| Zai Hui GAN College of Mathematics and Software Science,Sichuan Normal University,Chengdu ,P. R. China Mathematical College,Sichuan University,Chengdu ,P. R. China Jian ZHANG College of Mathematics and Software Science,Sichuan Normal University,Chengdu ,P. R. China. Sharp Conditions of Global Existence for Nonlinear Klein-Gordon Equations[J]. Acta Mathematica Sinica, 2005, 48(2): 311-318. DOI: cnki:ISSN:0583-1431.0.2005-02-013 |
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| Authors: | Zai Hui GAN College of Mathematics Software Science Sichuan Normal University Chengdu P. R. China Mathematical College Sichuan University Chengdu P. R. China Jian ZHANG College of Mathematics Software Science Sichuan Normal University Chengdu P. R. China |
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| Affiliation: | Zai Hui GAN College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China Mathematical College, Sichuan University, Chengdu 610064, P. R. China Jian ZHANG College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China |
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| Abstract: | This paper is concerned with the Cauchy problem for a class of nonlinear Klein-Gordon equations with several competing potential functions. In terms of the characteristics of the ground state, the sharp conditions for blowing up and global existence are derived out by applying the potential well argument and the concavity method. And the question that how small the initial data are, the global solutions exist is answered. |
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| Keywords: | Nonlinear Klein-Gordon equation Sharp condition Global existence |
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