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A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results.
@article{COCV_2005__11_2_180_0,
author = {Raymond, Jean-Pierre and Vanninathan, Muthusamy},
title = {Exact controllability in fluid-solid structure : the {Helmholtz} model},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {180--203},
publisher = {EDP-Sciences},
volume = {11},
number = {2},
year = {2005},
doi = {10.1051/cocv:2005006},
zbl = {1125.93007},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005006/}
}
TY - JOUR AU - Raymond, Jean-Pierre AU - Vanninathan, Muthusamy TI - Exact controllability in fluid-solid structure : the Helmholtz model JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2005 SP - 180 EP - 203 VL - 11 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005006/ DO - 10.1051/cocv:2005006 LA - en ID - COCV_2005__11_2_180_0 ER -
%0 Journal Article %A Raymond, Jean-Pierre %A Vanninathan, Muthusamy %T Exact controllability in fluid-solid structure : the Helmholtz model %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 180-203 %V 11 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005006/ %R 10.1051/cocv:2005006 %G en %F COCV_2005__11_2_180_0
Raymond, Jean-Pierre; Vanninathan, Muthusamy. Exact controllability in fluid-solid structure : the Helmholtz model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 180-203. doi: 10.1051/cocv:2005006
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