Comptes Rendus
Partial Differential Equations/Optimal Control
Remarks on the null controllability of the Burgers equation
[Remarques sur la contrôlabilité exacte à zéro de l'équation de Burgers]
Comptes Rendus. Mathématique, Volume 341 (2005) no. 4, pp. 229-232.

Dans le contexte de l'équation de Burgers avec contrôles distribués, on présente une estimation optimale du temps minimal de contrôlabilité T(r) des données initiales de norme ⩽r dans L2.

In the context of the Burgers equation with distributed controls, we present optimal estimates for the minimal time of controllability T(r) of the initial data of norm ⩽r in L2.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.06.005

Enrique Fernández-Cara 1 ; Sergio Guerrero 1

1 Dpto. E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
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Enrique Fernández-Cara; Sergio Guerrero. Remarks on the null controllability of the Burgers equation. Comptes Rendus. Mathématique, Volume 341 (2005) no. 4, pp. 229-232. doi : 10.1016/j.crma.2005.06.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.06.005/

[1] S. Anita; D. Tataru Null controllability for the dissipative semilinear heat equation, Appl. Math. Optim., Volume 46 (2002), pp. 97-105

[2] A. Fursikov; O.Yu. Imanuvilov Controllability of Evolution Equations, Lecture Notes, vol. 34, Seoul National University, Korea, 1996

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