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.
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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.