Volume 31, Issue 1
Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain

Xiangqing Zhao & Meng Bai

J. Part. Diff. Eq., 31 (2018), pp. 29-46.

Published online: 2018-07

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  • 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.

  • Keywords

High-order KdV equation Bourgain smoothing property exact controllability Slemrod’s feedback law exponential stabilizability

  • AMS Subject Headings

93B05 93D15 35Q53

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhao-xiangqing@163.com (Xiangqing Zhao)

baimengclare@qq.com (Meng Bai)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-29, author = {Zhao , Xiangqing and Bai , Meng }, title = {Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {1}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/12510.html} }
TY - JOUR T1 - Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain AU - Zhao , Xiangqing AU - Bai , Meng JO - Journal of Partial Differential Equations VL - 1 SP - 29 EP - 46 PY - 2018 DA - 2018/07 SN - 31 DO - http://dor.org/10.4208/jpde.v31.n1.3 UR - https://global-sci.org/intro/jpde/12510.html KW - High-order KdV equation KW - Bourgain smoothing property KW - exact controllability KW - Slemrod’s feedback law KW - exponential stabilizability AB -

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.

Xiangqing Zhao & Meng Bai. (2019). Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain. Journal of Partial Differential Equations. 31 (1). 29-46. doi:10.4208/jpde.v31.n1.3
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