Volume 21, Number 4, October-December 2015
|Page(s)||1076 - 1107|
|Published online||19 June 2015|
Internal controllability of the korteweg–de vries equation on a bounded domain
Instituto de Matemática, Universidade Federal do Rio de Janeiro,
C.P. 68530, Cidade Universitária, Ilha do Fundão, 21941-909
Rio de Janeiro (RJ),
2 Institut Elie Cartan, UMR 7502 UHP/CNRS/INRIA, BP 70239, 54506 Vandœuvre-les-Nancy cedex, France.
3 Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 boulevard Saint-Michel, 75272 Paris cedex 06, France.
Received: 27 January 2014
Revised: 23 October 2014
This paper is concerned with the control properties of the Korteweg–de Vries (KdV) equation posed on a bounded interval (0,L) with a distributed control. When the control region is an arbitrary open subdomain (l1,l2), we prove the null controllability of the KdV equation by means of a new Carleman inequality. As a consequence, we obtain a regional controllability result, which roughly tells us that any target function arbitrarily chosen on (0,l1) and null on (l2,L) is reachable. Finally, when the control region is a neighborhood of the right endpoint, an exact controllability result in a weighted L2-space is also established.
Mathematics Subject Classification: 35Q53 / 37K10 / 93B05 / 93D15
Key words: KdV equation / Carleman estimate / null controllability / exact controllability
© EDP Sciences, SMAI, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.