Raymond, Jean-Pierre; Vanninathan, Muthusamy Exact controllability in fluid-solid structure: the Helmholtz model. (English) Zbl 1125.93007 ESAIM, Control Optim. Calc. Var. 11, 180-203 (2005). Summary: A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results. Cited in 3 ReviewsCited in 10 Documents MSC: 93B05 Controllability 35B37 PDE in connection with control problems (MSC2000) 35L05 Wave equation 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74M05 Control, switches and devices (“smart materials”) in solid mechanics 76D55 Flow control and optimization for incompressible viscous fluids 93C20 Control/observation systems governed by partial differential equations Keywords:Fluid- solid structure; exact controllability × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] G. Avalos , I. Lasiecka , Exact controllability of structural acoustic interactions . J. Math. Pures Appl. 82 ( 2003 ) 1047 - 1073 . Zbl 1109.93004 · Zbl 1109.93004 · doi:10.1016/S0021-7824(03)00016-3 [2] V. Barbu , T. Precupanu , Convexity and Optimization in Banach Spaces , 2nd ed., D. Reidel, Dordrecht ( 1986 ). MR 860772 | Zbl 0594.49001 · Zbl 0594.49001 [3] A. Bensoussan , G. Da Prato , M.C. Delfour and S.K. Mitter , Representation and Control of Infinite Dimensional Systems . Birkhäuser, Boston 1 ( 1992 ). MR 2273323 | Zbl 0781.93002 · Zbl 0781.93002 [4] C. Conca , J. Planchard , B. Thomas and M. Vanninathan , Problèmes mathématiques en couplage fluide-structure . Eyrolles, Paris ( 1994 ). · Zbl 0824.73002 [5] C. Conca , J. Planchard and M. Vanninathan , Fluids and periodic structures . Masson and J. Wiley, Paris ( 1995 ). MR 1652238 | Zbl 0910.76002 · Zbl 0910.76002 [6] L. Cot , J.-P. Raymond and J. Vancostenoble , Exact controllability of an aeroacoustic model . In preparation. Zbl pre05213244 · Zbl 1235.93129 [7] R. Dautray and J.-L. Lions , Analyse Mathématique et Calcul Scientifique . Masson, Paris ( 1987 ). MR 918560 [8] P. Destuynder and E. Gout d’Henin , Existence and uniqueness of a solution to an aeroacoustic model . Chin. Ann. Math. 23B ( 2002 ) 11 - 24 . Zbl 1007.35078 · Zbl 1007.35078 · doi:10.1142/S0252959902000031 [9] E. Gout d’Henin , Ondes de Stoneley en interaction fluide-structure . Ph.D. Thesis, Université de Poitiers ( 2002 ). [10] J.-L. Lions , Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués . Masson, Paris ( 1988 ). Zbl 0653.93003 · Zbl 0653.93003 [11] S. Micu and E. Zuazua , Boundary controllability of a linear hybrid system arising in the control of noise . SIAM J. Control Optim. 35 ( 1997 ) 531 - 555 . Zbl 0888.35017 · Zbl 0888.35017 · doi:10.1137/S0363012996297972 [12] J.J. Moreau , Bounded variation in time , in Topics in Nonsmooth Mechanics, J.J. Moreau, P.D. Panagiotopoulos, G. Strang Eds. Birkhäuser, Boston ( 1988 ) 1 - 74 . Zbl 0657.28008 · Zbl 0657.28008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.