(untitled) (Journal of Partial Differential Equations, 2022)
In this paper, we show by Hilbert Uniqueness Method that the boundary value problem of fifth-order KdV equationalign*casesy_t-y_5 x =0, (x, t) (0,2 π) ×(0, T), y(t, 2 π)-y(t, 0) =h_0(t), y_x(t, 2 π)-y_x(t, 0) =h_1(t), y_2 x(t, 2 π)-y_2 x(t, 0) =h_2(t), y_3 x(t, 2 π)-y_3 x(t, 0) =h_3(t), y_4 x(t, 2 π)-y_4 x(t, 0) =h_4(t),casesalign* (with boundary data as control inputs) is exact controllability.