Controllability of systems of Stokes equations with one control force : existence of insensitizing controls

Sergio Guerrero

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 6, page 1029-1054
  • ISSN: 0294-1449

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Guerrero, Sergio. "Controllability of systems of Stokes equations with one control force : existence of insensitizing controls." Annales de l'I.H.P. Analyse non linéaire 24.6 (2007): 1029-1054. <http://eudml.org/doc/78765>.

@article{Guerrero2007,
author = {Guerrero, Sergio},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Carleman inequalities; Stokes system; controllability},
language = {eng},
number = {6},
pages = {1029-1054},
publisher = {Elsevier},
title = {Controllability of systems of Stokes equations with one control force : existence of insensitizing controls},
url = {http://eudml.org/doc/78765},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Guerrero, Sergio
TI - Controllability of systems of Stokes equations with one control force : existence of insensitizing controls
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 6
SP - 1029
EP - 1054
LA - eng
KW - Carleman inequalities; Stokes system; controllability
UR - http://eudml.org/doc/78765
ER -

References

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  2. [2] Bodart O., González-Burgos M., Pérez-García R., Existence of insensitizing controls for a semilinear heat equation with a superlinear nonlinearity, Comm. Partial Differential Equations29 (7–8) (2004) 1017-1050. Zbl1067.93035
  3. [3] de Teresa L., Insensitizing controls for a semilinear heat equation, Comm. Partial Differential Equations25 (1–2) (2000) 39-72. Zbl0942.35028
  4. [4] L. De Teresa, O. Kavian, Unique continuation principle for systems of parabolic equations, in preparation. Zbl1195.35080
  5. [5] Fernández-Cara E., González-Burgos M., Guerrero S., Puel J.-P., Null controllability of the heat equation with boundary Fourier conditions: The linear case, ESAIM Control Optim. Calc. Var.12 (3) (2006) 442-465. Zbl1106.93009MR2224822
  6. [6] Fernández-Cara E., Guerrero S., Imanuvilov O.Yu., Puel J.-P., Local exact controllability of the Navier–Stokes system, J. Math. Pures Appl. (9)83 (12) (2004) 1501-1542. Zbl1267.93020
  7. [7] E. Fernández-Cara, S. Guerrero, Local exact controllability of micropolar fluids, J. Math. Fluid Mech., doi:10.1007/s00021-005-0207-1. Zbl1133.35423MR2336077
  8. [8] E. Fernández-Cara, S. Guerrero, Global Carleman estimates for solutions of parabolic systems defined by transposition and some applications to controllability, AMRX Appl. Math. Res. Express 2006, Art. ID 75090, 31 pp. Zbl1113.35037MR2211406
  9. [9] Fursikov A.V., Imanuvilov O.Yu., Controllability of Evolution Equations, Lecture Notes, vol. 34, Seoul National University, Korea, 1996. Zbl0862.49004MR1406566
  10. [10] S. Guerrero, Null controllability of some systems of two parabolic equations with one control force, SIAM J. Control Optim., in press. Zbl1146.93011MR2309033
  11. [11] Imanuvilov O.Yu., Remarks on exact controllability for the Navier–Stokes equations, ESAIM Control Optim. Calc. Var.6 (2001) 39-72. Zbl0961.35104
  12. [12] Imanuvilov O.Yu., Yamamoto M., Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, Publ. Res. Inst. Math. Sci.39 (2) (2003) 227-274. Zbl1065.35079MR1987865
  13. [13] Ladyzenskaya O.A., The Mathematical Theory of Viscous Incompressible Flow, Translated from the Russian by Richard A. Silverman, Revised, English edition, Gordon and Breach Science Publishers, New York–London, 1963. Zbl0121.42701
  14. [14] Lions J.-L., Quelques notions dans l'analyse et le contrôle de systèmes à données incomplètes, in: Málaga, 1989, Proceedings of the XIth Congress on Differential Equations and Applications/First Congress on Applied Mathematics, Univ. Málaga, Málaga, 1990, pp. 43-54. Zbl0724.35050MR1096013
  15. [15] Lions J.-L., Sentinelles pour les systèmes distribués à données incomplètes, Recherches en Mathématiques Appliquées, vol. 21, Masson, Paris, 1992. Zbl0759.93043MR1159093
  16. [16] R. Pérez-García, Algunos resultados de control para algunos problemas parabólicos acoplados no lineales: controlabilidad y controles insensibilizantes, PhD Thesis, Sevilla, 2004. 
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