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Volume 35, Issue 2
Exact Boundary Controllability of Fifth-Order KdV Equation Posed on the Periodic Domain

Shuning Yang & Xiangqing Zhao

DOI: 10.4208/jpde.v35.n2.4

J. Part. Diff. Eq., 35 (2022), pp. 163-172.

Published online: 2022-04

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  • Abstract

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*}

(with boundary data as control inputs) is exact controllability.

  • Keywords

Fifth-order KdV equation, Hilbert Uniqueness Method, exact controllability.

  • AMS Subject Headings

93B05, 93D15, 35Q53

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangsn821@163.com (Shuning Yang)

zhao-xiangqing@163.com (Xiangqing Zhao)

  • BibTex
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  • TXT
@Article{JPDE-35-163, author = {Yang , Shuning and Zhao , Xiangqing}, title = {Exact Boundary Controllability of Fifth-Order KdV Equation Posed on the Periodic Domain}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {2}, pages = {163--172}, abstract = {

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*}

(with boundary data as control inputs) is exact controllability.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n2.4}, url = {http://global-sci.org/intro/article_detail/jpde/20449.html} }
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 -

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*}

(with boundary data as control inputs) is exact controllability.

Shuning Yang & Xiangqing Zhao. (2022). Exact Boundary Controllability of Fifth-Order KdV Equation Posed on the Periodic Domain. Journal of Partial Differential Equations. 35 (2). 163-172. doi:10.4208/jpde.v35.n2.4
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