一类五阶Korteweg-de-Vries方程的惟一连续性（英文）  

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

作　　者：高晓红[1,2] 郑晓翠[1,2] GAO Xiao-hong;ZHENG Xiao-cui(School of Mathematics, Northwest University, Xi'an 710127;Center for Nonlinear Studies, Northwest University, Xi'an 710069)

机构地区：[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

出　　处：《工程数学学报》2016年第5期541-550,共10页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11471259);the Natural Science Foundation of Shaanxi Province(2014JQ1002)

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Kd V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.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.

关 键 词：一类五阶Korteweg-de-Vries 方程 紧支集 惟一连续性 

分 类 号：O175.29[理学—数学]