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 
@article{JEMS_2013_15_4_a9,
     author = {J\'er\^ome Le Rousseau and Matthieu L\'eautaud and Luc Robbiano},
     title = {Controllability of a parabolic system with a diffuse interface},
     journal = {Journal of the European Mathematical Society},
     pages = {1485--1574},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2013},
     doi = {10.4171/jems/397},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/397/}
}
TY  - JOUR
AU  - Jérôme Le Rousseau
AU  - Matthieu Léautaud
AU  - Luc Robbiano
TI  - Controllability of a parabolic system with a diffuse interface
JO  - Journal of the European Mathematical Society
PY  - 2013
SP  - 1485
EP  - 1574
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/397/
DO  - 10.4171/jems/397
ID  - JEMS_2013_15_4_a9
ER  - 
%0 Journal Article
%A Jérôme Le Rousseau
%A Matthieu Léautaud
%A Luc Robbiano
%T Controllability of a parabolic system with a diffuse interface
%J Journal of the European Mathematical Society
%D 2013
%P 1485-1574
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/397/
%R 10.4171/jems/397
%F JEMS_2013_15_4_a9
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

Cité par Sources :