Geodesic
Controllability of a simplified model of fluid-structure interaction
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 547-575

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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.

DOI : 10.1051/cocv/2013075
Classification : 93B05, 93B07, 93C20, 74F10
Keywords: controllability, observability, fluid-structure interaction 
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     title = {Controllability of a simplified model of fluid-structure interaction},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {547--575},
     publisher = {EDP-Sciences},
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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

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