一个非线性色散波方程的惟一连续性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (6): 1523-1536.

一个非线性色散波方程的惟一连续性

1.西安交通大学理学院西安 710049;
2.西北大学数学系西安710069

收稿日期:2007-10-29 修回日期:2008-11-17 出版日期:2009-12-25 发布日期:2009-12-25
基金资助:
国家自然科学基金(10671153; 10671156)资助

On the Unique Continuation Property for a Nonlinear Dispersive System

1.School of Science,Xi'an Jiaotong University, Xi'an 710049;
2.Department of Mathematics, Northwest University, Xi'an 710069

Received:2007-10-29 Revised:2008-11-17 Online:2009-12-25 Published:2009-12-25
Supported by:
国家自然科学基金(10671153; 10671156)资助

摘要/Abstract

摘要：

该文证明: 和如下耦合色散系统相联系的初值问题的充分光滑的解$(u,v)=(u(x,t),v(x,t))$, 如果在两个时刻有半线支集那么它们全为零.
{∂ _tu+∂³_x u+∂ _x(u^p v^p⁺¹)=0,
∂_tv+∂³_x v+∂_x(u^p⁺¹v^p)=0, x ∈R, t ≥ 0

关键词: 耦合色散系统, 紧支集, 惟一连续性

Abstract:

It is proved that, if a sufficiently smooth solution $(u,v)=(u(x,t),v(x,t))$ to the initial value problem associated with the dispersive coupled system
{∂ _tu+∂³_x u+∂ _x(u^p v^p⁺¹)=0,
∂_tv+∂³_x v+∂_x(u^p⁺¹v^p)=0, x ∈R, t ≥ 0
is supported on a half line at two different instants of time then u ≡ 0, v ≡ 0.

Key words: Coupled dispersive system, Compact support, Unique continuation property

中图分类号:

35B30

付英, 马逸尘, 屈长征. 一个非线性色散波方程的惟一连续性[J]. 数学物理学报, 2009, 29(6): 1523-1536.

FU Ying, MA Yi-Chen, QU Chang-Zheng. On the Unique Continuation Property for a Nonlinear Dispersive System[J]. Acta mathematica scientia,Series A, 2009, 29(6): 1523-1536.