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| Instability of Standing Wave for the Klein–Gordon–Hartree Equation | |
| 作者姓名： | Xiao Guang LI ;Jian ZHANG ;Yong Hong WU |
| 作者单位： | [1]VisualComputingandVirtualRealityKeyLaboratorTlofSichuanProvince,SichuanNormalUniversity,Chengdu610066,P.R.China; [2]CollegeofMathematicsandSoftwareScience,SichuanNormalUniversity,Chengdu610066,P.R.China; [3]DepartmentofMathematicsandStatistics,CurtinUniversityofTechnology,Perth,WA6845,Australia |
| 基金项目： | The first author is supported by the Key Project of Chinese Ministry of Education(Grant No.211162);Sichuan Province Science Foundation for Youths(Grant No.2012JQ0011);the second author is supported byNational Natural Science Foundation of China(Grant No.11371267) |
| 摘 要： | The instability property of the standing wave uω(t, x) = eiωtφ(x) for the Klein–Gordon– Hartree equation |
| 关 键 词： | 不稳定 Klein 驻波 方程 稳定特性 有限时间 |
Instability of standing wave for the Klein-Gordon-Hartree equation |
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| Xiao Guang LI,;Jian ZHANG,;Yong Hong WU.Instability of standing wave for the Klein-Gordon-Hartree equation[J].Acta Mathematica Sinica,2014,30(5):861-871. | |
| Authors: | Xiao Guang Li Jian Zhang Yong Hong Wu |
| Institution: | 1. Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu, 610066, P. R. China 2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, P. R. China 3. Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA, 6845, Australia |
| Abstract: | The instability property of the standing wave u ω (t, x) = eiωt φ(x) for the Klein-Gordon-Hartree equation $$\frac{{\partial ^2 u}} {{\partial t^2 }} - \Delta u + u - \left( {\left| x \right|^{ - \gamma } *\left| u \right|^2 } \right)u = 0, x \in \mathbb{R}^N , 0 < \gamma < \min \left\{ {N,4} \right\}$$ is investigated. For the case N ≥ 3 and $\omega ^2 < \tfrac{2} {{N + 4 - \gamma }}$ , it is shown that the standing wave eiωt φ(X) is strongly unstable by blow-up in finite time. |
| Keywords: | Klein–Gordon–Hartree equation standing waves strong instability |
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