EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 29 (2023) ESAIM: COCV, 29 (2023) 31 References
Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 31
Number of page(s) 24
DOI https://doi.org/10.1051/cocv/2023014
Published online 28 April 2023
  1. F. Ammar-Khodja, A. Benabdallah, M. González-Burgos and L. de Teresa, Recent results on the controllability of linear coupled parabolic problems: a survey. Math. Control Relat. Fields 1 (2011) 267–306. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Ammar Khodja, A. Benabdallah, M. González-Burgos and L. de Teresa, Minimal time for the null controllability of parabolic systems: the effect of the condensation index of complex sequences. J. Funct. Anal. 267 (2014) 2077–2151. [Google Scholar]
  3. F. Ammar Khodja, A. Benabdallah, M. González-Burgos and L. de Teresa, New phenomena for the null controllability of parabolic systems: minimal time and geometrical dependence. j. Math. Anal. Appl. 444 (2016) 1071–1113. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Benabdallah, F. Boyer and M. Morancey, A block moment method to handle spectral condensation phenomenon in parabolic control problems. Ann. H. Lebesgue 3 (2020) 717–793. [CrossRef] [MathSciNet] [Google Scholar]
  5. N. Carreño, S. Guerrero and M. Gueye, Insensitizing controls with two vanishing components for the three-dimensional Boussinesq system. ESAIM: COCV 21 (2015) 73–100. [CrossRef] [EDP Sciences] [Google Scholar]
  6. N. Carreño and M. Gueye, Insensitizing controls with one vanishing component for the Navier-Stokes system. J. Math. Pures Appl. (9) 101 (2014) 27–53. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Conforto, L. Desvillettes and R. Monaco, Some asymptotic limits of reaction-diffusion systems appearing in reversible chemistry. Ric. Mat. 66 (2017) 99–111. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.-M. Coron and A.V. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary. Russ. J. Math. Phys. 4 (1996) 429–448. [Google Scholar]
  9. 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]
  10. J.-M. Coron and P. Lissy, Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components. Invent. Math. 198 (2014) 833–880. [Google Scholar]
  11. P. Érdi and J. Tóth, Mathematical models of chemical reactions, Nonlinear Science: Theory and Applications, Princeton University Press, Princeton, NJ (1989), theory and applications of deterministic and stochastic models. [Google Scholar]
  12. H.O. Fattorini and D.L. Russell, Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations. Quart. Appl. Math. 32 (1974/75) 45–69. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Fernaández-Cara, M. Gonzáalez-Burgos, S. Guerrero and J.-P. Puel, Null controllability of the heat equation with boundary Fourier conditions: the linear case. ESAIM: COCV 12 (2006) 442–465. [CrossRef] [EDP Sciences] [Google Scholar]
  14. E. Fernández-Cara, S. Guerrero, O.Y. Imanuvilov and J.-P. Puel, Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. (9) 83 (2004) 1501–1542. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Fernaández-Cara, S. Guerrero, O.Y. 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]
  16. A.V. Fursikov and O.Y. Imanuvilov, Controllability of evolution equations, Vol. 34 of Lecture Notes Series. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
  17. M. González-Burgos and L. de Teresa, Controllability results for cascade systems of m coupled parabolic PDEs by one control force. Port. Math. 67 (2010) 91–113. [CrossRef] [MathSciNet] [Google Scholar]
  18. S. Guerrero, Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions ESAIM: COCV 12 (2006) 484–544. [EDP Sciences] [Google Scholar]
  19. S. Guerrero, Controllability of systems of Stokes equations with one control force: existence of insensitizing controls. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007) 1029–1054. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Guerrero, Null controllability of some systems of two parabolic equations with one control force. SIAM J. Control Optim. 46 (2007) 379–394. [Google Scholar]
  21. S. Guerrero and C. Montoya, Local null controllability of the N-dimensional Navier-Stokes system with nonlinear Navier-slip boundary conditions and N - 1 scalar controls. J. Math. Pures Appl. (9) 113 (2018) 37–69. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Iida, H. Monobe, H. Murakawa and H. Ninomiya, Vanishing, moving and immovable interfaces in fast reaction limits. J. Differ. Equ. 263 (2017) 2715–2735. [CrossRef] [Google Scholar]
  23. O.Y. Imanuvilov, On exact controllability for the Navier-Stokes equations. ESAIM: COCV 3 (1998) 97–131. [CrossRef] [EDP Sciences] [Google Scholar]
  24. O.Y. Imanuvilov, Remarks on exact controllability for the Navier-Stokes equations. ESAIM: COCV 6 (2001) 39–72. [Google Scholar]
  25. O.Y. 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]
  26. G. Lebeau and L. Robbiano, Contrôle exacte de l’équation de la chaleur, in Séminaire sur les Équations aux Dérivées Partielles, 1994-1995, Exp. No. VII, 13, École Polytech., Palaiseau (1995). [Google Scholar]
  27. Y. Liu, T. Takahashi and M. Tucsnak, Single input controllability of a simplified fluid-structure interaction model. ESAIM: COCV 19 (2013) 20–42. [CrossRef] [EDP Sciences] [Google Scholar]
  28. C. Montoya and L. de Teresa, Robust Stackelberg controllability for the Navier-Stokes equations. NoDEA Nonlinear Differential Equations Appl. 25 (2018) Paper No. 46, 33. [CrossRef] [Google Scholar]
  29. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Vol. 44 of Applied Mathematical Sciences. Springer-Verlag, New York (1983). [CrossRef] [Google Scholar]
  30. H. Sohr, The Navier-Stokes equations, Modern Birkhäuser Classics, Birkhäuser/Springer Basel AG, Basel (2001), an elementary functional analytic approach, [2013 reprint of the 2001 original] [MR1928881]. [Google Scholar]
  31. T. Takahashi, Boundary local null-controllability of the Kuramoto-Sivashinsky equation. Math. Control Signals Syst. 29 (2017) Art. 2, 21. [CrossRef] [Google Scholar]
  32. R. Temam, Navier-Stokes equations. Vol. 2 of Studies in Mathematics and its Applications, revised edn., North-Holland Publishing Co., Amsterdam-New York (1979), theory and numerical analysis, With an appendix by F. Thomasset. [Google Scholar]
  33. M. Tucsnak and G. Weiss, Observation and control for operator semigroups, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhauser 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.