[Application de la contrôlabilité exacte à zéro de l'équation de la chaleur au déplacement d'ensembles]
On étudie la contrôlabilité lagrangienne de l'équation de la chaleur en toutes dimensions. En dimension 1, on montre que deux intervalles quelconques sont difféomorphes via le flot de la solution de l'équation de la chaleur avec un contrôle adéquat. En dimension supérieure on prouve un résultat de contrôlabilité similaire pour le flot du gradient, en temps fini fixé pour le cas radial, et en temps assez grand pour le cas convexe.
We study the lagrangian controllability of the heat equation in several dimensions. In dimension one, we prove that any pairs of intervals are diffeomorphic through the flow of the solution of the heat equation via an adequate control. In higher dimensions we prove a similar controllability result for the flow of the gradient of the solution in a radial case in arbitrary finite time, and for convex domains in a sufficiently large time.
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@article{CRMATH_2006__342_11_849_0,
author = {Thierry Horsin Molinaro},
title = {Application of the exact null controllability of the heat equation to moving sets},
journal = {Comptes Rendus. Math\'ematique},
pages = {849--852},
publisher = {Elsevier},
volume = {342},
number = {11},
year = {2006},
doi = {10.1016/j.crma.2006.04.001},
language = {en},
}
Thierry Horsin Molinaro. Application of the exact null controllability of the heat equation to moving sets. Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 849-852. doi : 10.1016/j.crma.2006.04.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.001/
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