Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain

Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain

Year:    2018

Author:    Xiangqing Zhao, Meng Bai

Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 1 : pp. 29–46

Abstract

In this paper, we study exact controllability and feedback stabilization for the distributed parameter control systemdescribed by high-order KdV equation posed on a periodic domain T with an internal control acting on an arbitrary small nonempty subdomain ω of T. On one hand, we show that the distributed parameter control system is locally exactly controllable with the help of Bourgain smoothing effect; on the other hand, we prove that the feedback system is locally exponentially stable with an arbitrarily large decay rate when Slemrod’s feedback input is chosen.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v31.n1.3

Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 1 : pp. 29–46

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    High-order KdV equation

Author Details

Xiangqing Zhao

Meng Bai

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