Instability of Standing Wave for the Klein–Gordon–Hartree Equation
The instability property of the standing wave u ω (t, x) = eiωt φ(x) for the Klein-Gordon-Hartree equation ∂ 2 u ∂t 2 −Δu+u− (|x| −γ *|u| 2 )u = 0, x ∈R N , 0<γ<min{N,4} is investigated. For the case N ≥ 3 and ω 2 <2 N+4−γ, it is shown that the standing wave eiωt φ(X) is strongly unstable...
| Main Authors: | , , |
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| Format: | Journal Article |
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Springer
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/16146 |
| _version_ | 1848749091388915712 |
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| author | Li, X. Zhang, J. Wu, Yong Hong |
| author_facet | Li, X. Zhang, J. Wu, Yong Hong |
| author_sort | Li, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The instability property of the standing wave u ω (t, x) = eiωt φ(x) for the Klein-Gordon-Hartree equation ∂ 2 u ∂t 2 −Δu+u− (|x| −γ *|u| 2 )u = 0, x ∈R N , 0<γ<min{N,4} is investigated. For the case N ≥ 3 and ω 2 <2 N+4−γ, it is shown that the standing wave eiωt φ(X) is strongly unstable by blow-up in finite time. |
| first_indexed | 2025-11-14T07:15:25Z |
| format | Journal Article |
| id | curtin-20.500.11937-16146 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:15:25Z |
| publishDate | 2014 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-161462017-09-13T15:04:06Z Instability of Standing Wave for the Klein–Gordon–Hartree Equation Li, X. Zhang, J. Wu, Yong Hong 35A15 standing waves 35L70 35B35 strong instability Klein-Gordon-Hartree equation The instability property of the standing wave u ω (t, x) = eiωt φ(x) for the Klein-Gordon-Hartree equation ∂ 2 u ∂t 2 −Δu+u− (|x| −γ *|u| 2 )u = 0, x ∈R N , 0<γ<min{N,4} is investigated. For the case N ≥ 3 and ω 2 <2 N+4−γ, it is shown that the standing wave eiωt φ(X) is strongly unstable by blow-up in finite time. 2014 Journal Article http://hdl.handle.net/20.500.11937/16146 10.1007/s10114-014-2399-x Springer restricted |
| spellingShingle | 35A15 standing waves 35L70 35B35 strong instability Klein-Gordon-Hartree equation Li, X. Zhang, J. Wu, Yong Hong Instability of Standing Wave for the Klein–Gordon–Hartree Equation |
| title | Instability of Standing Wave for the Klein–Gordon–Hartree Equation |
| title_full | Instability of Standing Wave for the Klein–Gordon–Hartree Equation |
| title_fullStr | Instability of Standing Wave for the Klein–Gordon–Hartree Equation |
| title_full_unstemmed | Instability of Standing Wave for the Klein–Gordon–Hartree Equation |
| title_short | Instability of Standing Wave for the Klein–Gordon–Hartree Equation |
| title_sort | instability of standing wave for the klein–gordon–hartree equation |
| topic | 35A15 standing waves 35L70 35B35 strong instability Klein-Gordon-Hartree equation |
| url | http://hdl.handle.net/20.500.11937/16146 |