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

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) is an element of(0,2 pi) x (0, T), y(t,2 pi)- y(t,0) = h(0)(t), y(x)(t, 2 pi)- y(x)(t, 0)= h(1)(t), y(2x)(t, 2 pi)- y(2x)( t,0)= h(2)(t), y(3x)(t, 2 pi)- y(3x)( t,0)= h(3)(t), y(4x)(t, 2 pi)- y(4x)( t,0)= h(4)(t), (with boundary data as control inputs) is exact controllability.