Approximate controllability of a hydro-elastic coupled system

Lions, Jacques-Louis, and Zuazua, Enrique. "Approximate controllability of a hydro-elastic coupled system." ESAIM: Control, Optimisation and Calculus of Variations 1 (2010): 1-15. <http://eudml.org/doc/197373>.

@article{Lions2010,
abstract = { We analyze the controllability of the motion of a fluid by means of the action of a vibrating shell coupled at the boundary of the fluid. The model considered is linear. We study its approximate controllability, i.e. whether the fluid may reach a dense set of final configurations at a given time. We show that this problem can be reduced to a unique continuation question for the Stokes system. We prove that this unique continuation property holds generically among analytic domains and therefore, that there is approximate controllability generically. We also prove that this result fails when Ω is a ball showing that the analyticity assumption on the domain is not sufficient. },
author = {Lions, Jacques-Louis, Zuazua, Enrique},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Hydroelasticity / approximate controllability / coupled system / spectral decomposition / generic spectral properties; Hydroelasticity; approximate controllability; coupled system; spectral decomposition; generic spectral properties; Stokes system},
language = {eng},
month = {3},
pages = {1-15},
publisher = {EDP Sciences},
title = {Approximate controllability of a hydro-elastic coupled system},
url = {http://eudml.org/doc/197373},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Lions, Jacques-Louis
AU - Zuazua, Enrique
TI - Approximate controllability of a hydro-elastic coupled system
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 1
EP - 15
AB - We analyze the controllability of the motion of a fluid by means of the action of a vibrating shell coupled at the boundary of the fluid. The model considered is linear. We study its approximate controllability, i.e. whether the fluid may reach a dense set of final configurations at a given time. We show that this problem can be reduced to a unique continuation question for the Stokes system. We prove that this unique continuation property holds generically among analytic domains and therefore, that there is approximate controllability generically. We also prove that this result fails when Ω is a ball showing that the analyticity assumption on the domain is not sufficient.
LA - eng
KW - Hydroelasticity / approximate controllability / coupled system / spectral decomposition / generic spectral properties; Hydroelasticity; approximate controllability; coupled system; spectral decomposition; generic spectral properties; Stokes system
UR - http://eudml.org/doc/197373
ER -