In this paper,we show by Hilbert Uniqueness Method that the boundary value problem of fifth-order KdV equation{y_(t)-y_(5x)=0,(x,t)∈(0,2π)×(0,T),y(t,2π)-y(t,0)=h_(0)(t),y_(x)(t,2π)-y_(x)(t,0)=h_(1)(t),y_(2x)(...In this paper,we show by Hilbert Uniqueness Method that the boundary value problem of fifth-order KdV equation{y_(t)-y_(5x)=0,(x,t)∈(0,2π)×(0,T),y(t,2π)-y(t,0)=h_(0)(t),y_(x)(t,2π)-y_(x)(t,0)=h_(1)(t),y_(2x)(t,2π)-y_(2x)(t,0)=h_(2)(t),y_(3x)(t,2π)-y_(3x)(t,0)=h_(3)(t),y_(4x)(t,2π)-y_(4x)(t,0)=h_(4)(t),(with boundary data as control inputs)is exact controllability.展开更多
基金supported by the Zhejiang Provincial Natural Science Foundation of China(No.LY18A010024)National Natural Science Foundation of China(No.12075208).
文摘In this paper,we show by Hilbert Uniqueness Method that the boundary value problem of fifth-order KdV equation{y_(t)-y_(5x)=0,(x,t)∈(0,2π)×(0,T),y(t,2π)-y(t,0)=h_(0)(t),y_(x)(t,2π)-y_(x)(t,0)=h_(1)(t),y_(2x)(t,2π)-y_(2x)(t,0)=h_(2)(t),y_(3x)(t,2π)-y_(3x)(t,0)=h_(3)(t),y_(4x)(t,2π)-y_(4x)(t,0)=h_(4)(t),(with boundary data as control inputs)is exact controllability.
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.