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Exact controllability in fluid – solid structure:The Helmholtz model

Published online by Cambridge University Press:  15 March 2005

Jean-Pierre Raymond  and
Muthusamy Vanninathan
Jean-Pierre Raymond
Affiliation:
Université Paul Sabatier, UMR 5640, Laboratoire MIP, 31062 Toulouse Cedex 4, France; [email protected]
Muthusamy Vanninathan
Affiliation:
IISc-TIFR Mathematics Programme, TIFR Centre, Bangalore 560012, India.
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Abstract

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 controlin 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.

Keywords

Fluid – solid structureexact controllability.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 2 , April 2005 , pp. 180 - 203
Copyright
© EDP Sciences, SMAI, 2005

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References

Avalos, G., Lasiecka, I., Exact controllability of structural acoustic interactions. J. Math. Pures Appl. 82 (2003) 1047–1073. CrossRef
V. Barbu, T. Precupanu, Convexity and Optimization in Banach Spaces, 2nd ed., D. Reidel, Dordrecht (1986).
A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Birkhäuser, Boston 1 (1992).
C. Conca, J. Planchard, B. Thomas and M. Vanninathan, Problèmes mathématiques en couplage fluide-structure. Eyrolles, Paris (1994).
C. Conca, J. Planchard and M. Vanninathan, Fluids and periodic structures. Masson and J. Wiley, Paris (1995).
L. Cot, J.-P. Raymond and J. Vancostenoble, Exact controllability of an aeroacoustic model. In preparation.
R. Dautray and J.-L. Lions, Analyse Mathématique et Calcul Scientifique. Masson, Paris (1987).
Destuynder, P. and Gout d'Henin, E., Existence and uniqueness of a solution to an aeroacoustic model. Chin. Ann. Math. 23B (2002) 11–24. CrossRef
E. Gout d'Henin, Ondes de Stoneley en interaction fluide-structure. Ph.D. Thesis, Université de Poitiers (2002).
J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Masson, Paris (1988).
Micu, S. and Zuazua, E., Boundary controllability of a linear hybrid system arising in the control of noise. SIAM J. Control Optim. 35 (1997) 531–555. CrossRef
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.