Remarks on the null controllability of the Burgers equation

Enrique Fernández-Cara; Sergio Guerrero

doi:10.1016/j.crma.2005.06.005

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]

Présenté par : Gilles Lebeau

Enrique Fernández-Cara ¹ ; Sergio Guerrero ¹

¹ Dpto. E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain

Comptes Rendus. Mathématique, Volume 341 (2005) no. 4, pp. 229-232.

Résumé
Abstract

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 $L^{2}$ .

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 $L^{2}$ .

Reçu le : 2005-05-12
Accepté le : 2005-05-31
Publié le : 2005-08-15

DOI : 10.1016/j.crma.2005.06.005

Affiliations des auteurs :

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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     author = {Enrique Fern\'andez-Cara and Sergio Guerrero},
     title = {Remarks on the null controllability of the {Burgers} equation},
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     pages = {229--232},
     publisher = {Elsevier},
     volume = {341},
     number = {4},
     year = {2005},
     doi = {10.1016/j.crma.2005.06.005},
     language = {en},
}

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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/

Bibliographie
Cité par

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Boris Andreianov; Shyam Sundar Ghoshal; Konstantinos Koumatos Lack of controllability of the viscous Burgers equation: part I—the $L^{\infty}$ setting, Journal of Evolution Equations, Volume 22 (2022) no. 3 | DOI:10.1007/s00028-022-00831-5
Sorin Micu; Takéo Takahashi Local controllability to stationary trajectories of a Burgers equation with nonlocal viscosity, Journal of Differential Equations, Volume 264 (2018) no. 5, p. 3664 | DOI:10.1016/j.jde.2017.11.029
Karl Kunisch; Lijuan Wang The bang-bang property of time optimal controls for the Burgers equation, Discrete Continuous Dynamical Systems - A, Volume 34 (2014) no. 9, p. 3611 | DOI:10.3934/dcds.2014.34.3611
Adimurthi; Shyam Sundar Ghoshal; G. D. Veerappa Gowda Exact controllability of scalar conservation laws with strict convex flux, Mathematical Control Related Fields, Volume 4 (2014) no. 4, p. 401 | DOI:10.3934/mcrf.2014.4.401
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S. Guerrero; O.Yu. Imanuvilov Remarks on global controllability for the Burgers equation with two control forces, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 24 (2007) no. 6, p. 897 | DOI:10.1016/j.anihpc.2006.06.010
Enrique Fernández-Cara; Sergio Guerrero Null controllability of the Burgers system with distributed controls, Systems Control Letters, Volume 56 (2007) no. 5, p. 366 | DOI:10.1016/j.sysconle.2006.10.022

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