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Controllability of a simplified model of fluid-structure interaction∗

Published online by Cambridge University Press:  28 March 2014

S. Ervedoza  and
M. Vanninathan
S. Ervedoza
Affiliation:
Institut de Mathématiques de Toulouse ; UMR5219; Université de Toulouse ; CNRS; UPS IMT, F-31062 Toulouse Cedex 9, France. ervedoza@math.univ-toulouse.fr; vanni@math.tifrbng.res.in
M. Vanninathan
Affiliation:
Institut de Mathématiques de Toulouse ; UMR5219; Université de Toulouse ; CNRS; UPS IMT, F-31062 Toulouse Cedex 9, France. ervedoza@math.univ-toulouse.fr; vanni@math.tifrbng.res.in
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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.

Keywords

Controllabilityobservabilityfluid-structure interaction
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 2 , April 2014 , pp. 547 - 575
Copyright
© EDP Sciences, SMAI, 2014

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