| Issue |
ESAIM: COCV
Volume 10, Number 3, July 2004
|
|
|---|---|---|
| Page(s) | 346 - 380 | |
| DOI | https://doi.org/10.1051/cocv:2004012 | |
| Published online | 15 June 2004 | |
Control of the surface of a fluid by a wavemaker
Institut Elie Cartan, Université Henri Poincaré Nancy 1,
BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France; rosier@iecn.u-nancy.fr.
Received:
10
April
2003
Revised:
12
November
2003
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in Lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Mathematics Subject Classification: 35B37 / 49J20 / 76B15 / 93B05 / 93C20
Key words: Korteweg-de Vries equation / Lagrangian coordinates / exact boundary controllability / Carleman estimate.
© EDP Sciences, SMAI, 2004
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