Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain  

作　　者：ZHAO Xiangqing BAI Meng 

机构地区：[1]Department of Mathematics, Zhejiang Ocean University, Zhoushan 316000, China. [2]Key Laboratory of Oceanographic Big Data Mining-& Application of Zhejiang Province, Zhoushan 316000, China. [3]School of Mathematics and Statistics Sciences, Zhaoqing University,Zhaoqing 526061, China.

出　　处：《Journal of Partial Differential Equations》2018年第1期29-46,共18页偏微分方程（英文版）

基　　金：The first author is financially supported by the Natural Science Foundation of Zhejiang Province （# LY18A010024, # LQ16A010003）, the China National Natural Science Foundation （# 11505154, # 11605156） and the Open Foundation from Marine Sciences in the Most Important Subjects of Zhejiang （# 20160101）. The second author is financially sup- ported by Foundation for Distinguished Young Teacher in Higher Education of Guangdong, China （YQ2015167）, Foundation for Characteristic Innovation in Higher Education of Guangdong, China （Analysis of some kinds of models of cell division and the spread of epidemics）, NSF of Guangdong Province （2015A030313707）. The authors are greatly in debt to the anonymous referee for his/her valuable comments and suggestions on modifying this manuscript.

摘　　要：In this paper, we study exact controllability and feedback stabilization forthe distributed parameter control system described by high-order KdV equation posedon a periodic domain T with an internal control acting on an arbitrary small nonemptysubdomain w of T. On one hand, we show that the distributed parameter controlsystem is locally exactly controllable with the help of Bourgain smoothing effect; onthe other hand, we prove that the feedback system is locally exponentially stable withan arbitrarily large decay rate when Slemrod＇s feedback input is chosen.

关 键 词：High-order KdV equation Bourgain smoothing property exact controllability Slem-rod＇s feedback law exponential stabilizability. 

分 类 号：O[理学]