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

top
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

top

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

top
  1. G. Avalos, I. Lasiecka, Exact controllability of structural acoustic interactions. J. Math. Pures Appl.82 (2003) 1047–1073.  
  2. V. Barbu, T. Precupanu, Convexity and Optimization in Banach Spaces, 2nd ed., D. Reidel, Dordrecht (1986).  
  3. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Birkhäuser, Boston 1 (1992).  
  4. C. Conca, J. Planchard, B. Thomas and M. Vanninathan, Problèmes mathématiques en couplage fluide-structure. Eyrolles, Paris (1994).  
  5. C. Conca, J. Planchard and M. Vanninathan, Fluids and periodic structures. Masson and J. Wiley, Paris (1995).  
  6. L. Cot, J.-P. Raymond and J. Vancostenoble, Exact controllability of an aeroacoustic model. In preparation.  
  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.  
  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).  
  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.  
  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.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.