Comptes Rendus
no. 3
Partial Differential Equations
Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients
[Inégalités de Carleman et résultats de contrôle pour une équation de la chaleur à coefficient BV en dimension un]

Présenté par : Gilles Lebeau

Jérôme Le Rousseau1
1 Laboratoire d'analyse topologie probabilités, CNRS UMR 6632, Université d'Aix-Marseille I, 13453 Marseille cedex 13, France
Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 175-180.

On obtient des inégalités de Carleman pour des opérateurs paraboliques linéaires ∂t±∂x(c∂x) avec un coefficient c à variations bornées. Ces inégalités sont obtenues par approximations de c par des coefficients réguliers par morceaux, cε, et en passant à la limite dans les inégalités de Carleman associées aux opérateurs définis par cε. De telles inégalités donnent des résultats de contrôlabilité aux trajectoires pour une classe d'équations semilinéaires paraboliques.

We derive global Carleman estimates for one-dimensional linear parabolic operators ∂t±∂x(c∂x) with a coefficient c with bounded variations. These estimates are obtained by approximating c by piecewise regular coefficients, cε, and passing to the limit in the Carleman estimates associated to the operators defined with cε. Such estimates yield results of controllability to the trajectories for a class of semilinear parabolic equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.12.011
Jérôme Le Rousseau 1

1 Laboratoire d'analyse topologie probabilités, CNRS UMR 6632, Université d'Aix-Marseille I, 13453 Marseille cedex 13, France 
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Jérôme Le Rousseau. Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients. Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 175-180. doi : 10.1016/j.crma.2006.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.12.011/

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