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