Geodesic
Controllability of a parabolic system with a diffuse interface
Journal of the European Mathematical Society, Tome 15 (2013) no. 4, pp. 1485-1574.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/397
Classification : 35-XX, 93-XX, 00-XX
Keywords: Elliptic operator, parabolic system, transmission problem, controllability, spectral inequality 
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     title = {Controllability of a parabolic system with a diffuse interface},
     journal = {Journal of the European Mathematical Society},
     pages = {1485--1574},
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Jérôme Le Rousseau; Matthieu Léautaud; Luc Robbiano. Controllability of a parabolic system with a diffuse interface. Journal of the European Mathematical Society, Tome 15 (2013) no. 4, pp. 1485-1574. doi : 10.4171/jems/397. http://geodesic.mathdoc.fr/articles/10.4171/jems/397/

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