Free Access
Volume 20, Number 3, July-September 2014
Page(s) 924 - 956
Published online 13 June 2014
  1. M. Badra, Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system. ESAIM: COCV 15 (2009) 934–968. [CrossRef] [EDP Sciences] [Google Scholar]
  2. M. Badra, Lyapunov function and local feedback boundary stabilization of the Navier-Stokes equations. SIAM J. Control Optim. 48 (2009) 1797–1830. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Badra, Abstract settings for stabilization of nonlinear parabolic system with a Riccati-based strategy. Application to Navier-Stokes and Boussinesq equations with Neumann or Dirichlet control. Discrete Contin. Dyn. Syst. – Series A 32 (2011) 1169–1208. [Google Scholar]
  4. M. Badra, Local controllability to trajectories of the magnetohydrodynamic equations. J. Math. Fluid Mech. (Sumitted). [Google Scholar]
  5. M. Badra and T. Takahashi, Stabilization of parabolic nonlinear systems with finite dimensional feedback or dynamical controllers. Application to the Navier-Stokes system. SIAM J. Control Optim. 49 (2011) 420–463. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Badra and T. Takahashi, Feedback stabilization of a fluid–rigid body interaction system. preprint. [Google Scholar]
  7. M. Badra and T. Takahashi, Feedback stabilization of a simplified 1d fluid – particle system. Ann. Inst. Henri Poincaré Anal. Non Linéaire (Sumitted). [Google Scholar]
  8. V. Barbu and R.L. Triggiani, Internal stabilization of Navier-Stokes equations with finite-dimensional controllers. Indiana Univ. Math. J. 53 (2004) 1443–1494. [CrossRef] [MathSciNet] [Google Scholar]
  9. V. Barbu, I. Lasiecka and R. Triggiani, Abstract settings for tangential boundary stabilization of Navier-Stokes equations by high- and low-gain feedback controllers. Nonlinear Anal. 64 (2006) 2704–2746. [CrossRef] [MathSciNet] [Google Scholar]
  10. V. Barbu, I. Lasiecka and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations. Mem. Amer. Math. Soc. 181 (2006) 128. [Google Scholar]
  11. V. Barbu, I. Lasiecka and R. Triggiani, Local exponential stabilization strategies of the Navier-Stokes equations, d = 2,3, via feedback stabilization of its linearization, in Control of coupled partial differential equations, vol. 155. Int. Ser. Numer. Math. Birkhäuser, Basel (2007) 13–46. [Google Scholar]
  12. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite dimensional systems. Systems & Control: Foundations & Applications. 2nd edition. Birkhäuser Boston Inc., Boston, MA (2007). [Google Scholar]
  13. J.-M. Coron and E. Trélat, Global steady-state controllability of one-dimensional semilinear heat equations. SIAM J. Control Optim. 43 (2004) 549–569. [CrossRef] [MathSciNet] [Google Scholar]
  14. R.F. Curtain and H. Zwart, An introduction to infinite-dimensional linear systems theory, vol. 21. Texts Appl. Math.. Springer-Verlag, New York (1995). [Google Scholar]
  15. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Vol. 5. Spectre des opérateurs. [The operator spectrum], With the collaboration of Michel Artola, Michel Cessenat, Jean Michel Combes and Bruno Scheurer, Reprinted from the 1984 edition. INSTN: Collection Enseignement. [INSTN: Teaching Collection]. Masson, Paris (1988). [Google Scholar]
  16. E.B. Davies, Pseudo-spectra, the harmonic oscillator and complex resonances. R. Soc. London Proc. Ser. A Math. Phys. Eng. Sci. 455 (1999) 585–599. [CrossRef] [Google Scholar]
  17. C. Fabre and G. Lebeau, Prolongement unique des solutions de l’equation de Stokes. Commun. Partial Differ. Eqs. 21 (1996) 573–596. [Google Scholar]
  18. H.O. Fattorini, Some remarks on complete controllability. SIAM J. Control 4 (1966) 686–694. [CrossRef] [MathSciNet] [Google Scholar]
  19. H.O. Fattorini, On complete controllability of linear systems. J. Differ. Eqs. 3 (1967) 391–402. [CrossRef] [Google Scholar]
  20. E. Fernández-Cara and S. Guerrero, Local exact controllability of micropolar fluids. J. Math. Fluid Mech. 9 (2007) 419–453. [CrossRef] [MathSciNet] [Google Scholar]
  21. E. Fernández-Cara, S. Guerrero, O. Yu. Imanuvilov and J.-P. Puel, Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. 83 (2004) 1501–1542. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.V. Fursikov, Stabilizability of a quasilinear parabolic equation by means of boundary feedback control. Mat. Sb. 192 (2001) 115–160. [CrossRef] [Google Scholar]
  23. A.V. Fursikov, Stabilizability of two-dimensional Navier-Stokes equations with help of a boundary feedback control. J. Math. Fluid Mech. 3 (2001) 259–301. [CrossRef] [MathSciNet] [Google Scholar]
  24. A.V. Fursikov, Stabilization for the 3D Navier-Stokes system by feedback boundary control. Partial differential equations and applications. Discrete Contin. Dyn. Syst. 10 (2004) 289–314. [CrossRef] [MathSciNet] [Google Scholar]
  25. G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I. Linearized steady problems, vol. 38. Springer Tracts in Natural Philosophy. Springer-Verlag, New York (1994). [Google Scholar]
  26. I.C. Gohberg and M.G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators. Translated from the Russian by A. Feinstein. Vol. 18. Translations of Mathematical Monographs. Amer. Math. Soc., Providence, R.I. (1969). [Google Scholar]
  27. G.H. Hardy and E.M. Wright, An introduction to the theory of numbers. Oxford University Press, Oxford, 6th edition (2008). Revised by D.R. Heath-Brown and J. H. Silverman, With a foreword by Andrew Wiles. [Google Scholar]
  28. M.L.J. Hautus, Controllability and observability conditions of linear autonomous systems. Nederl. Akad. Wetensch. Proc. Ser. A. Vol. 31 of Indag. Math. (1969) 443–448. [Google Scholar]
  29. A. Henrot and M. Pierre, Variation et optimisation de formes, Une analyse géométrique (A geometric analysis). Vol. 48. Mathématiques & Applications [Mathematics & Applications]. Springer, Berlin (2005). [Google Scholar]
  30. L. Hörmander, The analysis of linear partial differential operators I. Classics in Mathematics. Springer-Verlag, Berlin (2003). Distribution theory and Fourier analysis, Reprint of the 2nd edition (1990) [Springer, Berlin; MR1065993 (91m:35001a)]. [Google Scholar]
  31. O. Yu. Imanuvilov. Remarks on exact controllability for the Navier-Stokes equations. ESAIM: COCV 6 (2001) 39–72. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  32. O.Y. Imanuvilov and J.-P. Puel, Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems. Int. Math. Res. Not. 16 (2003) 883–913. [CrossRef] [Google Scholar]
  33. T. Kato, Perturbation theory for linear operators. Classics in Mathematics. Springer-Verlag, Berlin (1995). Reprint of the 1980 edition. [Google Scholar]
  34. I. Lasiecka and R. Triggiani, Control theory for partial differential equations: continuous and approximation theories. I, Abstract parabolic systems. Vol. 74. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2000). [Google Scholar]
  35. J. Le Rousseau and G. Lebeau, On Carleman estimates for elliptic and parabolic operators. applications to unique continuation and control of parabolic equations. ESAIM: COCV 18 (2012) 712–747. [CrossRef] [EDP Sciences] [Google Scholar]
  36. C.-G. Lefter, On a unique continuation property related to the boundary stabilization of magnetohydrodynamic equations. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 56 (2010) 1–15. [Google Scholar]
  37. G. Łukaszewicz, Micropolar fluids. Theory and applications. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston Inc., Boston, MA (1999). [Google Scholar]
  38. A.J. Meir, The equations of stationary, incompressible magnetohydrodynamics with mixed boundary conditions. Comput. Math. Appl. 25 (1993) 13–29. [CrossRef] [Google Scholar]
  39. A.M. Micheletti, Perturbazione dello spettro dell’operatore di Laplace, in relazione ad una variazione del campo. Ann. Scuola Norm. Sup. Pisa 26 (1972) 151–169. [MathSciNet] [Google Scholar]
  40. S. Micu and E. Zuazua, On the controllability of a fractional order parabolic equation. SIAM J. Control Optim. 44 (2006) 1950–1972. [CrossRef] [MathSciNet] [Google Scholar]
  41. A. Pazy, Semigroups of linear operators and applications to partial differential equations, vol. 44. Appl. Math. Sci. Springer-Verlag, New York (1983). [Google Scholar]
  42. J.-P. Raymond, Feedback boundary stabilization of the two-dimensional Navier-Stokes equations. SIAM J. Control Optim. 45 (2006) 790–828. [CrossRef] [MathSciNet] [Google Scholar]
  43. J.-P. Raymond and T. Thevenet, Boundary feedback stabilization of the two dimensional Navier-Stokes equations with finite dimensional controllers. Issue in Discrete and Continuous Dynamical Systems A 27 (2010) 1159–1187. [CrossRef] [Google Scholar]
  44. D.L. Russell and G. Weiss, A general necessary condition for exact observability. SIAM J. Control Optim. 32 (1994) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
  45. H. Triebel, Interpolation theory, function spaces, differential operators, 2nd edition. Johann Ambrosius Barth, Heidelberg (1995). [Google Scholar]
  46. R. Triggiani, On the stabilizability problem in Banach space. J. Math. Anal. Appl. 52 (1975) 383–403,. [CrossRef] [MathSciNet] [Google Scholar]
  47. R. Triggiani, Extensions of rank conditions for controllability and observability to Banach spaces and unbounded operators. SIAM J. Control Optim. 14 (1976) 313–338. [CrossRef] [Google Scholar]
  48. R. Triggiani, Boundary feedback stabilizability of parabolic equations. Appl. Math. Optim. 6 (1980) 201–220. [CrossRef] [MathSciNet] [Google Scholar]
  49. R. Triggiani, Unique continuation from an arbitrary interior subdomain of the variable-coefficient Oseen equation. Nonlinear Anal. 71 (2009) 4967–4976. [CrossRef] [MathSciNet] [Google Scholar]
  50. M. Tucsnak and G. Weiss, Observation and control for operator semigroups. Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser Verlag, Basel (2009). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.