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

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

Year:    2022

Author:    Shuning Yang, Xiangqing Zhao

Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 2 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v35.n2.4

Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 2 : pp. 163–172

Published online:    2022-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Fifth-order KdV equation Hilbert Uniqueness Method exact controllability.

Author Details

Shuning Yang

Xiangqing Zhao