Controllability of a simplified model of fluid-structure interaction

S. Ervedoza; M. Vanninathan

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 2, page 547-575
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Ervedoza, S., and Vanninathan, M.. "Controllability of a simplified model of fluid-structure interaction." ESAIM: Control, Optimisation and Calculus of Variations 20.2 (2014): 547-575. <http://eudml.org/doc/272824>.

@article{Ervedoza2014,
abstract = {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.},
author = {Ervedoza, S., Vanninathan, M.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {controllability; observability; fluid-structure interaction},
language = {eng},
number = {2},
pages = {547-575},
publisher = {EDP-Sciences},
title = {Controllability of a simplified model of fluid-structure interaction},
url = {http://eudml.org/doc/272824},
volume = {20},
year = {2014},
}

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
PB - EDP-Sciences
VL - 20
IS - 2
SP - 547
EP - 575
AB - 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.
LA - eng
KW - controllability; observability; fluid-structure interaction
UR - http://eudml.org/doc/272824
ER -

References

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