| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 38 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2018033 | |
| Published online | 13 September 2019 | |
Control and stabilization of the periodic fifth order Korteweg-de Vries equation
1
California State University, Channel Islands, Bell Tower East 2762, One University Drive,
Camarillo,
CA
93012, USA.
2
Bâtiment des Mathématiques, EPFL, Station 8,
CH-1015
Lausanne, Switzerland.
* Corresponding author: derek.smith@epfl.ch
Received:
20
June
2017
Accepted:
16
May
2018
We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in Hs(𝕋), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regularity property, yields a smoothing effect permitting the application of the contraction principle.
Mathematics Subject Classification: 35Q53 / 93B05 / 93D15
Key words: Korteweg-de Vries equation / periodic domain / propagation of regularity / exact controllability / stabilization
© EDP Sciences, SMAI 2019
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