This article aims at studying the controllability of a simplified fluid structure interaction model derived and developed in [C. Conca, J. Planchard and M. Vanninathan, RAM: Res. Appl. Math. John Wiley & Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, ESAIM: COCV 11 (2005) 180-203; M. Tucsnak and M. Vanninathan, Systems Control Lett. 58 (2009) 547-552]. This interaction is modeled by a wave equation surrounding a harmonic oscillator. Our main result states that, in the radially symmetric case, this system can be controlled from the outer boundary. This improves previous results [J.-P. Raymond and M. Vanninathan, ESAIM: COCV 11 (2005) 180-203; M. Tucsnak and M. Vanninathan, Systems Control Lett. 58 (2009) 547-552]. Our proof is based on a spherical harmonic decomposition of the solution and the so-called lateral propagation of the energy for 1d waves.
Mots clés : controllability, observability, fluid-structure interaction
@article{COCV_2014__20_2_547_0,
author = {Ervedoza, S. and Vanninathan, M.},
title = {Controllability of a simplified model of fluid-structure interaction},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {547--575},
publisher = {EDP-Sciences},
volume = {20},
number = {2},
year = {2014},
doi = {10.1051/cocv/2013075},
mrnumber = {3264216},
zbl = {1285.93019},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2013075/}
}
TY - JOUR AU - Ervedoza, S. AU - Vanninathan, M. TI - Controllability of a simplified model of fluid-structure interaction JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 547 EP - 575 VL - 20 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2013075/ DO - 10.1051/cocv/2013075 LA - en ID - COCV_2014__20_2_547_0 ER -
%0 Journal Article %A Ervedoza, S. %A Vanninathan, M. %T Controllability of a simplified model of fluid-structure interaction %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 547-575 %V 20 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2013075/ %R 10.1051/cocv/2013075 %G en %F COCV_2014__20_2_547_0
Ervedoza, S.; Vanninathan, M. Controllability of a simplified model of fluid-structure interaction. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 547-575. doi : 10.1051/cocv/2013075. http://www.numdam.org/articles/10.1051/cocv/2013075/
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