# Controllability of a parabolic system with a diffuse interface

Jérôme Le Rousseau; Matthieu Léautaud; Luc Robbiano

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 4, page 1485-1574
- ISSN: 1435-9855

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topLe 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 -

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