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Séminaire Laurent Schwartz — EDP et applications

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Jérôme Le Rousseau; Matthieu Léautaud; Luc Robbiano
Controllability of a parabolic system with a diffusive interface
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exp. No. 17, 20 p., doi: 10.5802/slsedp.13
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Résumé - 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 $.

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