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| Instability of Standing Waves for Hamiltonian Wave Equations |
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Citation： |
Zaihui GAN,Boling GUO,Jie XIN.Instability of Standing Waves for Hamiltonian Wave Equations[J].Chinese Annals of Mathematics B,2010,31(2):219~230 |
| Page view： 1698
Net amount： 1642 |
Authors： |
Zaihui GAN; Boling GUO; Jie XIN; |
Foundation： |
the National Natural Science Foundation of China (No. 10801102, 10771151), the
Sichuan Youth Sciences and Technology Foundation (No. 07ZQ026-009) and the China Postdoctoral
Science Foundation. |
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| Abstract： |
This paper deals with the standing wave for a Hamiltonian nonlinear wave
equation which can be viewed as a representative of the class of equations of interest.
On the one hand, by proving a compactness lemma and solving a variational problem,
the existence of the standing wave with ground state for the aforementioned equation is
proved. On the other hand, the authors derive the instability of the standing wave by
applying the potential well argument, the concavity method and an invariant region under
the solution flow of the Cauchy problem for the equation under study, and the invariance
of the region aforementioned can be shown by introducing an auxiliary functional and a
supplementary constrained variational problem. |
Keywords： |
Hamiltonian wave equation, Ground state, Standing wave, Instability |
Classification： |
35A15, 35B25, 35J60 |
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