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

Abstract

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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.

How to cite

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Raymond, 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

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  6. L. Cot, J.-P. Raymond and J. Vancostenoble, Exact controllability of an aeroacoustic model. In preparation.  Zbl1235.93129
  7. R. Dautray and J.-L. Lions, Analyse Mathématique et Calcul Scientifique. Masson, Paris (1987).  
  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.  Zbl1007.35078
  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).  Zbl0653.93002
  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.  Zbl0888.35017
  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.  

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