Comptes Rendus
no. 10
Partial differential equations/Optimal control
Internal null-controllability of the N-dimensional heat equation in cylindrical domains

Presented by: Jean-Michel Coron

El Hadji Samb1
1 Laboratoire I2M, Institut de mathématiques de Marseille, UMR 7373, 13453 Marseille, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 925-930.

In this Note, we consider the internal null-controllability of the N-dimensional heat equation on domains of the form Ω=Ω1×Ω2, with Ω1=(0,1) and Ω2 a smooth domain of RN−1,N>1. When the control is exerted on γ={x0}×ω2⊂Ω, with x0 an algebraic real number of order d>1 and ω2⊊Ω2 a non-empty open subset, we show the null-controllability, for all time T>0. This result is obtained through the Lebeau–Robbiano strategy and requires an upper bound of the cost of the one-dimensional null-control.

Dans cette note, on considère la contrôlabilité à zéro interne de l'équation de la chaleur N-dimensionnelle, sur des domaines de la forme Ω=Ω1×Ω2, avec Ω1=(0,1) et Ω2 un domaine borné et régulier de RN−1,N>1. Lorsque le contrôle est exercé sur γ={x0}×ω2⊂Ω, avec x0 un nombre réel algébrique de degré d>1 et ω2⊊Ω2 un ouvert non vide, on montre la contrôlabilité à zéro, en tout temps T>0. Ce résultat s'appuie sur la stratégie de Lebeau–Robbiano et exige une estimation du coût du contrôle monodimensionnel.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.04.021

El Hadji Samb 1

1 Laboratoire I2M, Institut de mathématiques de Marseille, UMR 7373, 13453 Marseille, France 
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El Hadji Samb. Internal null-controllability of the N-dimensional heat equation in cylindrical domains. Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 925-930. doi : 10.1016/j.crma.2015.04.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.021/

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