Controllability of a parabolic system with a diffusive interface

Jérôme Le Rousseau[1]; Matthieu Léautaud[2]; Luc Robbiano[3]

  • [1] Université d’Orléans Laboratoire de Mathématiques - Analyse Probabilités, Modélisation - Orléans, CNRS UMR 7349 Fédération Denis-Poisson, FR CNRS 2964 B.P. 6759 45067 Orléans cedex 2 France
  • [2] Université Paris-Sud Mathématiques, Bâtiment 425 91405 Orsay Cedex France
  • [3] Université de Versailles Saint-Quentin Laboratoire de Mathématiques de Versailles CNRS UMR 8100 45 Avenue des États-Unis 78035 Versailles France

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-20
  • ISSN: 2266-0607

Abstract

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We consider a linear parabolic transmission problem across an interface of codimension one in a bounded domain or on a Riemannian manifold, where the transmission conditions involve an additional parabolic operator on the interface. This system is an idealization of a three-layer model in which the central layer has a small thickness δ . We prove a Carleman estimate in the neighborhood of the interface for an associated elliptic operator by means of partial estimates in several microlocal regions. In turn, from the Carleman estimate, we obtain a spectral inequality that yields the null-controllability of the parabolic system. These results are uniform with respect to the small parameter δ .

How to cite

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Le Rousseau, Jérôme, Léautaud, Matthieu, and Robbiano, Luc. "Controllability of a parabolic system with a diffusive interface." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-20. <http://eudml.org/doc/251187>.

@article{LeRousseau2011-2012,
abstract = {We consider a linear parabolic transmission problem across an interface of codimension one in a bounded domain or on a Riemannian manifold, where the transmission conditions involve an additional parabolic operator on the interface. This system is an idealization of a three-layer model in which the central layer has a small thickness $\delta $. We prove a Carleman estimate in the neighborhood of the interface for an associated elliptic operator by means of partial estimates in several microlocal regions. In turn, from the Carleman estimate, we obtain a spectral inequality that yields the null-controllability of the parabolic system. These results are uniform with respect to the small parameter $\delta $.},
affiliation = {Université d’Orléans Laboratoire de Mathématiques - Analyse Probabilités, Modélisation - Orléans, CNRS UMR 7349 Fédération Denis-Poisson, FR CNRS 2964 B.P. 6759 45067 Orléans cedex 2 France; Université Paris-Sud Mathématiques, Bâtiment 425 91405 Orsay Cedex France; Université de Versailles Saint-Quentin Laboratoire de Mathématiques de Versailles CNRS UMR 8100 45 Avenue des États-Unis 78035 Versailles France},
author = {Le Rousseau, Jérôme, Léautaud, Matthieu, Robbiano, Luc},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {transmission problem; Carleman estimate; null controllability},
language = {eng},
pages = {1-20},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Controllability of a parabolic system with a diffusive interface},
url = {http://eudml.org/doc/251187},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Le Rousseau, Jérôme
AU - Léautaud, Matthieu
AU - Robbiano, Luc
TI - Controllability of a parabolic system with a diffusive interface
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 20
AB - We consider a linear parabolic transmission problem across an interface of codimension one in a bounded domain or on a Riemannian manifold, where the transmission conditions involve an additional parabolic operator on the interface. This system is an idealization of a three-layer model in which the central layer has a small thickness $\delta $. We prove a Carleman estimate in the neighborhood of the interface for an associated elliptic operator by means of partial estimates in several microlocal regions. In turn, from the Carleman estimate, we obtain a spectral inequality that yields the null-controllability of the parabolic system. These results are uniform with respect to the small parameter $\delta $.
LA - eng
KW - transmission problem; Carleman estimate; null controllability
UR - http://eudml.org/doc/251187
ER -

References

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