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GLOBAL SMOOTH SOLUTIONS FOR SEMILINEAR SCHR（~DINGER EQUATIONS WITH BOUNDARY FEEDBACK ON 2-DIMENSIONAL RIEMANNIAN MANIFOLDS
  • ISSN号：1009-6124
  • 期刊名称：《系统科学与复杂性学报：英文版》
  • 时间：0
  • 分类：O413.1[理学—理论物理;理学—物理] Q959.21[生物学—动物学]
  • 作者机构：[1]Key Laboratory of Control and Systems, Institute of Systems Science, Academy of Mathematics and SystemsScience, Chinese Academy of Sciences, Beijing 100190, China, Graduate School of the Chinese Academy ofSciences, Beijing 100049, China, [2]Key Laboratory of Control and Systems, Institute of Systems Science, Academy of Mathematics and SystemsScience, Beijing 100190, China
  • 相关基金：This research is supported by the National Science Foundation of China under Grants Nos. 60225003, 60334040, 60221301, 60774025, and 10831007, and Chinese Academy of Sciences under Grant No KJCX3-SYW-S01.
作者： Li DENG[1], Pengfei YAO[2]
关键词： 全局光滑解, 薛定谔方程, 边界反馈, 黎曼流形, 半线性, 人道主义, 反应, 黎曼度量, Boundary feedback, energy decay, Riemannian metric, semilinear schr6dinger equation.
中文摘要：

当起始的数据是小的时，这篇论文在 2-dimensional Riemannian manifolds 上与边界反馈认为半的全球光滑的解决方案的存在是线性 schrödinger 方程。作者证明全球答案的存在边界反馈取决于不仅，而且在一个 Riemannian 度量标准上，由原则部分和原来的度量标准的系数给歧管。特别地， authers 证明系统的精力指数地腐烂。

英文摘要：

This paper considers the existence of global smooth solutions of semilinear schrSdinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the existence of global solutions depends not only on the boundary feedback, but also on a Riemannian metric, given by the coefficient of the principle part and the original metric of the manifold. In particular, the authers prove that the energy of the system decays exponentially.

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期刊信息
  • 《系统科学与复杂性学报：英文版》
  • 主管单位:中国科学院
  • 主办单位:中国科学院系统科学研究所
  • 主编：
  • 地址：北京东黄城根北街16号
  • 邮编：100080
  • 邮箱：
  • 电话：010-62541831 62541834
  • 国际标准刊号：ISSN：1009-6124
  • 国内统一刊号：ISSN：11-4543/O1
  • 邮发代号:82-545
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国工程索引,美国科学引文索引（扩展库）,英国科学文摘数据库
  • 被引量:125