Free Access
Issue
ESAIM: COCV
Volume 21, Number 1, January-March 2015
Page(s) 73 - 100
DOI https://doi.org/10.1051/cocv/2014020
Published online 17 October 2014
  1. V.M. Alekseev, V.M. Tikhomirov and S.V. Fomin., Optimal Control, Translated from the Russian by V.M. Volosov, Contemporary Soviet Mathematics. Consultants Bureau, New York (1987). [Google Scholar]
  2. O. Bodart and C. Fabre, Controls insensitizing the norm of the solution of a semilinear heat equation. J. Math. Anal. Appl. 195 (1995) 658–683. [CrossRef] [MathSciNet] [Google Scholar]
  3. N. Carreño, Local controllability of the N-dimensional Boussinesq system with N − 1 scalar controls in an arbitrary control domain. Math. Control Relat. Fields 2 (2012) 361–382. [CrossRef] [MathSciNet] [Google Scholar]
  4. N. Carreño and S. Guerrero, Local null controllability of the N-dimensional Navier−Stokes system with N − 1 scalar controls in an arbitrary control domain. J. Math. Fluid Mech. 15 (2013) 139–153. [CrossRef] [MathSciNet] [Google Scholar]
  5. N. Carreño and M. Gueye, Insensitizing controls with one vanishing component for the Navier−Stokes system. J. Math. Pures Appl. 101 (2014) 27–53. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.-M. Coron and S. Guerrero, Null controllability of the N-dimensional Stokes system with N − 1 scalar controls. J. Differ. Equ. 246 (2009) 2908–2921. [CrossRef] [Google Scholar]
  7. J.-M. Coron and P. Lissy, Local null controllability of the three-dimensional Navier−Stokes system with a distributed control having two vanishing components. To appear in Invent. Math. [Google Scholar]
  8. J.I. Díaz and A.V. Fursikov, Approximate controllability of the Stokes system on cylinders by external unidirectional forces. J. Math. Pures Appl. 9 (1997) 353–375. [CrossRef] [Google Scholar]
  9. E. Fernández-Cara, S. Guerrero, O. Yu. Imanuvilov and J.-P. Puel, Some controllability results for the N-dimensional Navier−Stokes and Boussinesq systems with N − 1 scalar controls. SIAM J. Control Optim. 45 (2006) 146–173. [CrossRef] [MathSciNet] [Google Scholar]
  10. A.V. Fursikov O. Yu. Imanuvilov. Controllability of Evolution Equations. Lecture Notes #34. Seoul National University, Korea (1996). [Google Scholar]
  11. S. Guerrero, Controllability of systems of Stokes equations with one control force: existence of insensitizing controls. Ann. Inst. Henri Poincaré Anal. Non Linéaire 24 (2007) 1029–1054. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Gueye, Insensitizing controls for the Navier−Stokes equations. Ann. Inst. Henri Poincaré Anal. Non Linéaire 30 (2013) 825–844. [Google Scholar]
  13. O. Yu. Imanuvilov, Remarks on exact controllability for the Navier−Stokes equation. ESAIM: COCV 6 (2001) 39–37. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. O. Yu. Imanuvilov, J.-P. Puel and M. Yamamoto, Carleman estimates for parabolic equations with nonhomogeneous boundary conditions. Chin. Ann. Math. Ser. B 30 (2009) 333–378. [CrossRef] [MathSciNet] [Google Scholar]
  15. O. Kavian and L. de Teresa, Unique continuation principle for systems of parabolic equations. ESAIM: COCV 16 (2010) 247–274. [CrossRef] [EDP Sciences] [Google Scholar]
  16. O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, revised English edition, translated from the Russian by Richard A. Silverman. Gordon and Breach Science Publishers, New York, London (1963). [Google Scholar]
  17. O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural’ceva, Linear and quasilinear equations of parabolic type, Translated from the Russian by S. Smith. Vol. 23 of Translations of Mathematical Monographs. American Mathematical Society, Providence, R.I. (1968). [Google Scholar]
  18. J.-L. Lions, Quelques notions dans l’analyse et le contrôle de systèmes à données incomplètes (Somes notions in the analysis and control of systems with incomplete data). Proc. of the XIth congress on Differential Equations and Applications/First Congress on Applied Mathematics, Málaga (1989). Univ. Málaga (1990) 43–54. [Google Scholar]
  19. J.-L. Lions, Sentinelles pour les systèmes distribués à données incomplètes (Sentinelles for Distributed Systems with Incomplete Data). Vol. 21 of Recherches en Mathématiques Appliquées (Research in Applied Mathematics). Masson, Paris (1992). [Google Scholar]
  20. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 2, Travaux et Recherches Mathématiques, No. 18. Dunod, Paris (1968). [Google Scholar]
  21. J.-L. Lions and E. Zuazua, A generic uniqueness result for the Stokes system and its control theoretical consequences, Partial differential equations and applications. Vol. 177 of Lect. Notes Pure Appl. Math. Dekker, New York (1996) 221–235. [Google Scholar]
  22. S. Micu, J.H. Ortega and L. de Teresa, An example of ε-insensitizing controls for the heat equation with no intersecting observation and control regions. Appl. Math. Lett. 17 (2004) 927–932. [CrossRef] [Google Scholar]
  23. R. Pérez-García, Nuevos resultados de control para algunos problemas parabólicos acoplados no lineales: controlabilidad y controles insensibilizantes. Ph.D. thesis, University of Seville, Spain, 2004. [Google Scholar]
  24. J.-C. Saut and B. Scheurer, Unique continuation for some evolution equations. J. Differ. Equ. 66 (1987) 118–139. [Google Scholar]
  25. R. Temam, Navier−Stokes Equations, Theory and Numerical Analysis. Vol. 2 of Study Math. Appl. North-Holland, Amsterdam, New York, Oxford (1977). [Google Scholar]
  26. L. de Teresa, Insensitizing controls for a semilinear heat equation. Commun. Partial Differ. Equ. 25 (2000) 39–72. [Google Scholar]

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