Optimal Control/Partial Differential Equations
Global controllability of nonviscous Burgers type equations
Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 241-246.

We are interested in the global controllability of nonviscous Burgers type equations on a bounded interval. We have three controls: two are the boundary values, one is the right member of the equation and is constant with respect to the space variable. It has already been shown that boundary controls are not sufficient to have global controllability in small time. We prove here that the introduction of this new control in the right member of the equation allows us to obtain global controllability, even in small time.

On s'intéresse à la contrôlabilité globale d'équations du type Burgers non visqueuses sur un intervalle borné. Nous avons trois contrôles : les deux valeurs au bord et le membre de droite de l'équation, supposé constant par rapport à la variable d'espace. Il a déjà été démontré que des contrôles au bord ne suffisent pas pour obtenir la contrôlabilité globale en temps petit. Nous montrons ici que l'introduction de ce nouveau contrôle dans le membre de droite permet d'avoir contrôlabilité globale pour tout temps.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.12.016
Chapouly, Marianne 1

1 Département de mathématique, bâtiment 425, université Paris-Sud 11, 91405 Orsay cedex, France
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Chapouly, Marianne. Global controllability of nonviscous Burgers type equations. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 241-246. doi : 10.1016/j.crma.2006.12.016. http://www.numdam.org/articles/10.1016/j.crma.2006.12.016/

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