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Null-controllability for a Coupled Heat-Finite-dimensional Beam System

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Optimal Control of Coupled Systems of Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 158))

Abstract

A model representing a coupling between a heat conducting medium and a finite-dimensional approximation of a beam equation is considered. We establish a Carleman inequality for this model. Next we deduce a nullcontrollability result with an internal control in the conducting medium and there is no control in the structure equation.

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References

  1. M. Boulakia and A. Osses, Local null controllability of a two-dimensional fluid-structure interaction problem, ESAIM COCV, 14(1) (2008), 1–42.

    Article  MathSciNet  Google Scholar 

  2. C. Conca, J. Planchard, B. Thomas, and M. Vanninathan., Problèmes mathématiques en couplage fluide-structure, Eyrolles, Paris, 1994.

    MATH  Google Scholar 

  3. C. Conca, J. Planchard, and M. Vanninathan, Fluids and periodic structures, Masson and J. Wiley, Paris, 1995.

    MATH  Google Scholar 

  4. O. Yu. Èmanuvilov, Controllability of parabolic equations, Mat. Sbornik, 186(6) (1995), 109–132.

    MathSciNet  Google Scholar 

  5. A.V. Fursikov, Optimal Control of distributed systems. Theory and Applications, Translations of Mathematical Monographs # 187, AMS Providence RI, 2000.

    MATH  Google Scholar 

  6. A.V. Fursikov and O.Yu. Imanuvilov., Controllability of evolution equations, Lecture Notes series 34, Seoul National University, Research Institute of Mathematics, Global Analysis Research Centre, Seoul 1996.

    MATH  Google Scholar 

  7. O. Imanuvilov and T. Takahashi, Exact controllability of a fluid-rigid body system, J. Math. Pures Appl., 87 (2007), 408–437.

    Article  MathSciNet  Google Scholar 

  8. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Masson, Paris, 1988.

    MATH  Google Scholar 

  9. J.-P. Raymond and M. Vanninathan, Exact controllability in fluid-solid structure: the Helmholtz model, ESAIM Control Optim. Calc. Var., 11(2) (2005), 180–203 (electronic).

    Article  MathSciNet  Google Scholar 

  10. J.-P. Raymond and M. Vanninathan, Null Controllability in a Heat-Solid Structure Model, Applied Math. Optim., 2008, DOI 10.1007/s00245-008-9053-x.

    Google Scholar 

  11. J.-P. Raymond and M. Vanninathan, Null Controllability in a Fluid-Solid Structure Model, in preparation.

    Google Scholar 

  12. J.C. Saut and B. Scheurer, Unique Continuation for some evolution equations, J. Diff. Equations, 66 (1987), 118–139.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. UPS, Institut de Mathématiques, Université de Toulouse, F-31062, Toulouse Cedex 9, France

    Jean-Pierre Raymond

  2. Institut de Mathématiques, UMR 5219, CNRS, F-31062, Toulouse Cedex 9, France

    Jean-Pierre Raymond

  3. TIFR-CAM, Post Bag 6503, Bangalore, 560065, India

    Muthusamy Vanninathan

Authors
  1. Jean-Pierre Raymond
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  2. Muthusamy Vanninathan
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Editor information

Editors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Karl Kunisch

  2. Abt. Partielle Differentialgleichung Weierstraß-Institut für Angewandte Analysis und Stochastik, Humboldt-Universität zu Berlin, Mohrenstrasse 39, 10117, Berlin, Germany

    Jürgen Sprekels

  3. LS Angewandte Mathematik II Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstrasse 3, 91058, Erlangen, Germany

    Günter Leugering

  4. Institut für Mathematik Fak. II Mathematik & Naturwissenschaften, TU Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Fredi Tröltzsch

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Raymond, JP., Vanninathan, M. (2009). Null-controllability for a Coupled Heat-Finite-dimensional Beam System. In: Kunisch, K., Sprekels, J., Leugering, G., Tröltzsch, F. (eds) Optimal Control of Coupled Systems of Partial Differential Equations. International Series of Numerical Mathematics, vol 158. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-8923-9_13

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