Global smooth solutions for the quasilinear wave equation with boundary dissipation
文献类型：期刊论文
| 作者 | Yao, Peng-Fei
|
| 刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2007-10-01 |
| 卷号 | 241期号:1页码:62-93 |
| 关键词 | quasilinear wave equation Riemannian metric dissipative boundary structure |
| ISSN号 | 0022-0396 |
| DOI | 10.1016/j.jde.2007.06.014 |
| 英文摘要 | We consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input-output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system. Our main tool is the geometrical analysis. The main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system. We show that the existence of global solutions depends not only on this dissipation structure but also on a Riemannian metric, given by the coefficients and the equilibrium of the system. Some geometrical conditions on this Riemannian metric are presented to guarantee the existence of global solutions. In particular, we prove that the norm of the state of the system decays exponentially if the input stops after a finite time, which implies the exponential stabilization of the system by boundary feedback. (c) 2007 Elsevier Inc. All rights reserved. |
| 语种 | 英语 |
| WOS记录号 | WOS:000250232500003 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/4826]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Yao, Peng-Fei |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Control & Syst, Beijing 100081, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yao, Peng-Fei. Global smooth solutions for the quasilinear wave equation with boundary dissipation[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2007,241(1):62-93. |
| APA | Yao, Peng-Fei.(2007).Global smooth solutions for the quasilinear wave equation with boundary dissipation.JOURNAL OF DIFFERENTIAL EQUATIONS,241(1),62-93. |
| MLA | Yao, Peng-Fei."Global smooth solutions for the quasilinear wave equation with boundary dissipation".JOURNAL OF DIFFERENTIAL EQUATIONS 241.1(2007):62-93. |
入库方式： OAI收割
来源：数学与系统科学研究院
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