Controllability of a simplified model of fluid-structure interaction∗
Revised: 13 August 2013
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.
Mathematics Subject Classification: 93B05 / 93B07 / 93C20 / 74F10
Key words: Controllability / observability / fluid-structure interaction
The first author is partially supported by the Agence Nationale de la Recherche (ANR, France), Project CISIFS number NT09-437023. The second author is supported by CEFIPRA within the Project 3701-1 Control of Systems of Partial Differential Equations. He also thanks French CNRS and Institut de Mathématiques de Toulouse for hospitality and support for his stay in France during which this work was carried out. Both authors acknowledge the support of the Indo-French Centre for Applied Mathematics (IFCAM).
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