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: Controllability, -- observability, -- fluid-structure interaction; 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 : 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.