Exact Boundary Controllability of Fifth-order KdV Equation Posed on the Periodic Domain

摘要

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.