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. [CrossRef] [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] [MathSciNet] [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]

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