Comptes Rendus
no. 19-20
Partial Differential Equations/Optimal Control
Boundary null-controllability of linear diffusion–reaction equations
[Contrôlabilité frontière à zéro des équations linéaires de type diffusion–réaction]

Présenté par : Jean-Michel Bony

Adel Hamdi1 ; Imed Mahfoudhi1
1 Laboratoire de mathématiques LMI, INSA de Rouen, avenue de l'université, BP 8, 76801 St-Etienne-du-Rouvray cedex, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1083-1086.

Il s'agit de la contrôlabilité frontière à zéro des équations linéaires de type diffusion–réaction dans un domaine borné de R2. Nous transformons la détermination du contrôle de type HUM en la minimisation d'une fonctionnelle continue et strictement convexe. Dans le cas d'un domaine rectangulaire où le tenseur de diffusion est représenté par une matrice diagonale, nous exprimons explicitement le contrôle recherché dans une base orthonormée construite par les fonctions propres d'un problème de Sturm–Liouville.

This Note deals with the boundary null-controllability of linear diffusion–reaction equations in a 2D bounded domain. We transform the determination of the sought HUM boundary control into the minimization of a continuous and strictly convex functional. In the case of a rectangular domain where the diffusion tensor is represented by a diagonal matrix, we establish a procedure based on the inner product method that uses a complete orthonormal family of Sturm–Liouville's eigenfunctions to express explicitly the sought control.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.09.019

Adel Hamdi 1 ; Imed Mahfoudhi 1

1 Laboratoire de mathématiques LMI, INSA de Rouen, avenue de l'université, BP 8, 76801 St-Etienne-du-Rouvray cedex, France 
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Adel Hamdi; Imed Mahfoudhi. Boundary null-controllability of linear diffusion–reaction equations. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1083-1086. doi : 10.1016/j.crma.2010.09.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.019/

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  • Adel Hamdi Inverse source problem in a 2D linear evolution transport equation: detection of pollution source, Inverse Problems in Science and Engineering, Volume 20 (2012) no. 3, p. 401 | DOI:10.1080/17415977.2011.637207

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