一类七阶浅水波方程的惟一连续性（英文）

Unique Continuation Property for a Class of Seventh-order Shallow Water Wave Equations

Cauchy问题解的性质与初值的性质密切相关,而该问题解的惟一连续性是可积系统的重要性质之一.本文考虑一类七阶浅水波方程的Cauchy问题,该方程用来描述弱色散非线性长波沿水平方向的传播.本文的目的是研究该Cauchy问题解的惟一连续性.基于复变量技巧和Paley-Wiener定理,本文证明了该Cauchy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 properties of Cauchy problems are closely related with those of the initial values. The unique continuation properties of these problems are one of the important properties of the solution to the integrable system. Considered herein is the Cauchy problem associated with a class of seventh-order shallow water wave equations, which describe the propagation of weakly dispersive nonlinear long waves in the horizontal direction. The purpose here is to investigate the unique continuation property of the solutions to this Cauchy problem. Based on the complex variables technique and Paley-Wiener Theorem, it is proved that, if a sufficiently smooth solution to this Cauchy problem is supported compactly in a nontrivial time interval, then it vanishes identically.