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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (5): 541-550.doi: 10.3969/j.issn.1005-3085.2016.05.009

• • 上一篇    

一类五阶Korteweg-de-Vries方程的惟一连续性

高晓红1,2,  郑晓翠1,2   

  1. 1- 西北大学数学学院， 西安 710127
    2- 西北大学非线性研究中心，西安 710069
  • 收稿日期:2015-01-23 接受日期:2015-07-02 出版日期:2016-10-05 发布日期:2016-12-15
  • 基金资助:
    国家自然科学基金 (11471259)；陕西省自然科学基金 (2014JQ1002).

Unique Continuation Property for a Class of Fifth-order Korteweg-de-Vries Equations

GAO Xiao-hong1,2,  ZHENG Xiao-cui1,2   

  1. 1- School of Mathematics, Northwest University, Xi'an 710127
    2- Center for Nonlinear Studies, Northwest University, Xi'an 710069
  • Received:2015-01-23 Accepted:2015-07-02 Online:2016-10-05 Published:2016-12-15
  • Supported by:
    The National Natural Science Foundation of China (11471259); the Natural Science Foundation of Shaanxi Province (2014JQ1002).

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摘要： 惟一连续性是可积系统的重要性质之一，而初值问题解的性质与初值的光滑性密切相关．本文主要讨论了一类五阶KdV方程初值问题解的惟一连续性，证明了该初值问题的足够光滑的解，如果在一个非退化的时间区间内具有紧支集，那么该解恒为零．

关键词: 一类五阶Korteweg-de-Vries方程, 紧支集, 惟一连续性

Abstract: The unique continuation property is one of the important properties of the solutions to the integrable systems. The properties of the solutions of the initial value problems are bound up with the smoothness of the initial values. In this paper, we mainly discuss the unique continuation property of the solutions to the initial value problem associated with a class of fifth-order KdV equations. We prove that, if a sufficiently smooth solution to the initial value problem associated with the fifth-order Korteweg-de-Vries equations is supported compactly in a nontrivial time interval, then it vanishes identically.

Key words: a class of fifth-order Korteweg-de-Vries equations, compact support, unique continuation property

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