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Internal controllability of the Korteweg-de Vries equation on a bounded domain

Authors: R.A. Capistrano-Filho, A.F. Pazoto and Lionel Rosier, ESAIM Control Optim. Calc. Var., Vol. 21 No 4, pp. 1076-1107, 2015 DOI 10.1051/cocv/2014059
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.
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BibTeX:
@Article{2016-01-25,
author = {A.F. Pazoto and Lionel Rosier R.A. Capistrano-Filho},
title = {Internal controllability of the Korteweg-de Vries equation on a bounded domain},
journal = {ESAIM Control Optim. Calc. Var.},
volume = {21},
number = {4},
pages = {1076-1107},
year = {2015},
}