非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up |
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引用本文: | 赵军生,柳洪志.非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up[J].数学学报,2008,51(4):711-720. |
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作者姓名: | 赵军生 柳洪志 |
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作者单位: | 黑龙江大学数学科学学院,内蒙古财经学院统计与数学学院 哈尔滨 150080,呼和浩特 010051 |
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摘 要: | 研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果.
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关 键 词: | Klein-Gordon方程 位势井 整体解 存在性 |
收稿时间: | 2006-5-29 |
修稿时间: | 2007-7-24 |
Global Existence and Blow-up for Solutions for Cauchy Problem of Nonlinear Klein-Gordon Equations |
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Institution: | Jun Sheng ZHAO School of Mathematical Science,Heilongjiang University,Harbin 150080,P.R.China Hong Zhi LIU Department of Statistics and Mathematics,Finance and Economics Institute of the Inner Mongol,Huhehaote 010051,P.R.China |
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Abstract: | We study the Cauchy problem of nonlinear Klein-Gordon equation u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0; u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n. By introducing a family of potential wells we obtain a threshold result of global existence and nonexistcnce of solutions. |
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Keywords: | Klein-Gordon equations potential well global solution existence |
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