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| instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities | |
| Zaihui Gan; Boling Guo; Zhang Jian | |
| 2009 | |
| Source | Journal of Differential Equations
 |
| Volume | 246Issue:10Pages:4097-4128 |
| English Abstract | This paper discusses the Klein–Gordon–Zakharov system with different-degree nonlinearities in two and three space dimensions. Firstly, we prove the existence of standing wave with ground state by applying an intricate variational argument. Next, by introducing an auxiliary functional and an equivalent minimization problem, we obtain two invariant manifolds under the solution flow generated by the Cauchy problem to the aforementioned Klein–Gordon–Zakharov system. Furthermore, by constructing a type of constrained variational problem, utilizing the above two invariant manifolds as well as applying potential well argument and concavity method, we derive a sharp threshold for global existence and blowup. Then, combining the above results, we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation. Finally, we prove a modified instability of standing wave to the system under study. |
| Keyword | Klein–gordon–zakharov System Standing Wave Global Existence Blowup Instability |
| Department | 计算机科学国家重点实验室 |
| Language | 英语 |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/3140 |
| Collection | 基础软件与系统重点实验室 |
| Recommended Citation GB/T 7714 | Zaihui Gan,Boling Guo,Zhang Jian. instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities[J]. Journal of Differential Equations,2009,246(10):4097-4128. |
| APA | Zaihui Gan,Boling Guo,&Zhang Jian.(2009).instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities.Journal of Differential Equations,246(10),4097-4128. |
| MLA | Zaihui Gan,et al."instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities".Journal of Differential Equations 246.10(2009):4097-4128. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| 2009246104097.pdf（305KB） | 开放获取 | -- | Application Full Text | |||
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