Open Access
Volume 26, 2020
Article Number 3
Number of page(s) 18
Published online 13 January 2020
  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. [Google Scholar]
  4. F. Ammar Khodja, A. Benabdallah, M. González-Burgos and M. Morancey, Quantitative fattorini-hautus test and minimal null control time for parabolic problems. J. Math. Pures Appl. 9 (2017). [Google Scholar]
  5. K. Beauchard and P. Cannarsa, Heat equation on the Heisenberg group: observability and applications. J. Differ. Equ. 262 (2017) 4475–4521. [Google Scholar]
  6. K. Beauchard and K. Pravda-Starov, Null-controllability of hypoelliptic quadratic differential equations. J. Éc. Polytech. Math. 5 (2018) 1–43. [Google Scholar]
  7. K. Beauchard, P. Cannarsa and R. Guglielmi, Null controllability of Grushin-type operators in dimension two. J. Eur. Math. Soc. 16 (2014) 67–101. [CrossRef] [MathSciNet] [Google Scholar]
  8. K. Beauchard, B. Helffer, R. Henry and L. Robbiano, Degenerate parabolic operators of Kolmogorov type with a geometric control condition. ESAIM: COCV 21 (2015) 487–512. [CrossRef] [EDP Sciences] [Google Scholar]
  9. K. Beauchard, L. Miller and M. Morancey, 2D Grushin-type equations: minimal time and null controllable data. J. Differ. Equ. 259 (2015) 5813–5845. [Google Scholar]
  10. K. Beauchard, J. Dardé and S. Ervedoza, Minimal time issues for the observability of Grushin-type equations. Preprint (2018). [Google Scholar]
  11. P. Cannarsa, P. Martinez and J. Vancostenoble, Global Carleman estimates for degenerate parabolic operators with applications. Mem. Am. Math. Soc. 239 (2016) ix+209. [Google Scholar]
  12. J.-M. Coron, Control and Nonlinearity. Vol. 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2007). [Google Scholar]
  13. 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]
  14. S. Dolecki, Observability for the one-dimensional heat equation. Stud. Math. 48 (1973) 291–305. [CrossRef] [Google Scholar]
  15. M. Duprez, Controllability of a 2 × 2 parabolicsystem by one force with space-dependent coupling term of order one. ESAIM: COCV 23 (2017) 1473–1498. [CrossRef] [EDP Sciences] [Google Scholar]
  16. M. Duprez and P. Lissy, Positive and negative results on the internal controllability of parabolic equations coupled by zero- and first-order terms. J. Evol. Equ. 18 (2018) 659–680. [CrossRef] [Google Scholar]
  17. H.O. Fattorini and D.L. Russell, Exact controllability theorems for linear parabolic equations in one space dimension. Arch. Ratl. Mech. Anal. 43 (1971) 272–292. [CrossRef] [Google Scholar]
  18. E. Fernández-Cara, M. González-Burgos and L. de Teresa Boundary controllability of parabolic coupled equations. J. Funct. Anal. 259 (2010) 1720–1758. [Google Scholar]
  19. A.V. Fursikov and O.Yu. 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]
  20. M. González-Burgos and R. Pérez-García, Controllability results for some nonlinear coupled parabolic systems by one control force. Asymptot. Anal. 46 (2006) 123–162. [Google Scholar]
  21. A. Koenig, Non-null-controllability of the Grushin operator in 2D. C. R. Math. Acad. Sci. Paris 355 (2017) 1215–1235. [CrossRef] [Google Scholar]
  22. G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur. Commun. Part. Differ. Equ. 20 (1995) 335–356. [CrossRef] [Google Scholar]
  23. M. Morancey, Approximate controllability for a 2D Grushin equation with potential having an internal singularity. Ann. Inst. Fourier (Grenoble) 65 (2015) 1525–1556. [CrossRef] [Google Scholar]
  24. W. Rudin, Real and complex analysis. McGraw Hill Education, 3rd edition (1986). [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.