LOCAL CONTROLLABILITY OF THE KORTEWEG-DE VRIES EQUATION WITH THE RIGHT DIRICHLET CONTROL
Résumé
The Korteweg-de Vries (KdV) equation with the right Dirichlet control was initially investigated by Glass and Guerrero. They showed that this system is small time locally exactly controllable for all non critical lengths and its linearized system is not controllable for all critical lengths. Even the controllability of the KdV system has been studied extensively in the last two decades, the local controllability of this system for critical lengths remains an open question. In this paper, we give a definitive answer to this question. More precisely, we show that the KdV equation with the right Dirichlet control is finite time locally exactly controllable but not small time locally null controllable for all critical lengths.
Mots clés
Controllability KdV equations critical lengths unreachable space power series expansion Hilbert uniqueness method AMS subject classification: 35C20 35Q53 93B05 93B07 93C20
Controllability
KdV equations
critical lengths
unreachable space
power series expansion
Hilbert uniqueness method AMS subject classification: 35C20
35Q53
93B05
93B07
93C20
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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Licence |