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 . 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 .
@article{SLSEDP_2011-2012____A17_0,
author = {Le Rousseau, J\'er\^ome and L\'eautaud, Matthieu and Robbiano, Luc},
title = {Controllability of a parabolic system with a diffusive interface},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:17},
pages = {1--20},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2011-2012},
doi = {10.5802/slsedp.13},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.13/}
}
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 N1 - talk:17 PY - 2011-2012 SP - 1 EP - 20 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.13/ DO - 10.5802/slsedp.13 LA - en ID - SLSEDP_2011-2012____A17_0 ER -
%0 Journal Article %A Le Rousseau, Jérôme %A Léautaud, Matthieu %A Robbiano, Luc %T Controllability of a parabolic system with a diffusive interface %J Séminaire Laurent Schwartz — EDP et applications %Z talk:17 %D 2011-2012 %P 1-20 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.13/ %R 10.5802/slsedp.13 %G en %F SLSEDP_2011-2012____A17_0
Le Rousseau, Jérôme; Léautaud, Matthieu; Robbiano, Luc. Controllability of a parabolic system with a diffusive interface. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 17, 20 p. doi : 10.5802/slsedp.13. http://www.numdam.org/articles/10.5802/slsedp.13/
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