TY - JOUR
T1 - Exact Boundary Controllability of Fifth-Order KdV Equation Posed on the Periodic Domain
AU - Yang , Shuning
AU - Zhao , Xiangqing
JO - Journal of Partial Differential Equations
VL - 2
SP - 163
EP - 172
PY - 2022
DA - 2022/04
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n2.4
UR - https://global-sci.org/intro/article_detail/jpde/20449.html
KW - Fifth-order KdV equation, Hilbert Uniqueness Method, exact controllability.
AB - <p style="text-align: justify;">In this paper, we show by Hilbert Uniqueness Method that the boundary value problem of fifth-order KdV equation\begin{align*}\begin{cases}y_{t}-y_{5 x} =0, \quad(x, t) \in(0,2 \pi) \times(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_{2 x}(t, 2 \pi)-y_{2 x}(t, 0) =h_{2}(t),\\y_{3 x}(t, 2 \pi)-y_{3 x}(t, 0) =h_{3}(t),\\y_{4 x}(t, 2 \pi)-y_{4 x}(t, 0) =h_{4}(t),\end{cases}\end{align*}</p><p style="text-align: justify;">(with boundary data as control inputs) is exact controllability.</p>