# Exact controllability in fluid – solid structure: The Helmholtz model

Jean-Pierre Raymond; Muthusamy Vanninathan

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 2, page 180-203
- ISSN: 1292-8119

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topRaymond, Jean-Pierre, and Vanninathan, Muthusamy. "Exact controllability in fluid – solid structure: The Helmholtz model." ESAIM: Control, Optimisation and Calculus of Variations 11.2 (2010): 180-203. <http://eudml.org/doc/90760>.

@article{Raymond2010,

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 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.
},

author = {Raymond, Jean-Pierre, Vanninathan, Muthusamy},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Fluid – solid structure; exact controllability.; Fluid- solid structure; exact controllability},

language = {eng},

month = {3},

number = {2},

pages = {180-203},

publisher = {EDP Sciences},

title = {Exact controllability in fluid – solid structure: The Helmholtz model},

url = {http://eudml.org/doc/90760},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Raymond, Jean-Pierre

AU - Vanninathan, Muthusamy

TI - Exact controllability in fluid – solid structure: The Helmholtz model

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 2

SP - 180

EP - 203

AB -
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.

LA - eng

KW - Fluid – solid structure; exact controllability.; Fluid- solid structure; exact controllability

UR - http://eudml.org/doc/90760

ER -

## References

top- G. Avalos, I. Lasiecka, Exact controllability of structural acoustic interactions. J. Math. Pures Appl.82 (2003) 1047–1073.
- 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).
- P. Destuynder and E. Gout d'Henin, Existence and uniqueness of a solution to an aeroacoustic model. Chin. Ann. Math.23B (2002) 11–24.
- 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).
- 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.
- 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.

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