Controllability of a parabolic system with a diffuse interface

Le Rousseau, Jérôme, Léautaud, Matthieu, and Robbiano, Luc. "Controllability of a parabolic system with a diffuse interface." Journal of the European Mathematical Society 015.4 (2013): 1485-1574. <http://eudml.org/doc/277476>.

@article{LeRousseau2013,
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 $.},
author = {Le Rousseau, Jérôme, Léautaud, Matthieu, Robbiano, Luc},
journal = {Journal of the European Mathematical Society},
keywords = {elliptic operator; parabolic system; transmission problem; controllability; spectral inequality; parabolic operator on the interface; Carleman estimate; transmission problem; spectral inequality; parabolic operator on the interface; Carleman estimate},
language = {eng},
number = {4},
pages = {1485-1574},
publisher = {European Mathematical Society Publishing House},
title = {Controllability of a parabolic system with a diffuse interface},
url = {http://eudml.org/doc/277476},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Le Rousseau, Jérôme
AU - Léautaud, Matthieu
AU - Robbiano, Luc
TI - Controllability of a parabolic system with a diffuse interface
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 4
SP - 1485
EP - 1574
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 - elliptic operator; parabolic system; transmission problem; controllability; spectral inequality; parabolic operator on the interface; Carleman estimate; transmission problem; spectral inequality; parabolic operator on the interface; Carleman estimate
UR - http://eudml.org/doc/277476
ER -