Controllability of a simplified model of fluid-structure interaction∗. (7th April 2014)

• Record Type: Journal Article
• Authors: Ervedoza, S.; Vanninathan, M.
• Is Part Of: ESAIM. Volume 20:Number 2(2014:Apr.)
• Page Start: 547
• Page End: 575
• Publication Date: 2014-04-07
• Subjects: System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2013075
• Languages: English
• ISSNs: 1292-8119

Abstract

<abstract abstract-type="normal" xml:lang="en"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>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, <italic>RAM: Res. Appl. Math. </italic>John Wiley &amp; Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, <italic>ESAIM: COCV </italic><bold>11 </bold>(2005) 180–203; M. Tucsnak and M. Vanninathan, <italic>Systems Control Lett. </italic><bold>58 </bold>(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, <italic>ESAIM: COCV </italic><bold>11 </bold>(2005) 180–203; M. Tucsnak and M. Vanninathan, <italic>Systems Control Lett. </italic><bold>58 </bold>(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.</p> </abstract>