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All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 16 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 16
Number of page(s) 30
DOI https://doi.org/10.1051/cocv/2022009
Published online 24 February 2022
  1. R.A. Adams and J.J.F. Fournier, Vol. 140 of Sobolev spaces. Second edition, Pure and Applied Mathematics (Amsterdam). Elsevier/ Press, Amsterdam (2003). [Google Scholar]
  2. P. Alphonse, Régularité des solutions et contrôlabilité d’équations d’évolution associées à des opérateurs non-autoadjoints. Ph.D Thesis, University of Rennes 1, France (2020). [Google Scholar]
  3. P. Alphonse and J. Bernier, Smoothing properties of fractional Ornstein-Uhlenbeck semigroups and null-controllability. Bull. Sci. Math. 165 (2020). [Google Scholar]
  4. K. Beauchard, M. Egidi and K. Pravda-Starov, Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports. C. R. Math. Acad. Sci. Paris 358 (2020) 651–700. [MathSciNet] [Google Scholar]
  5. K. Beauchard, P. Jaming and K. Pravda-Starov, Spectral inequality for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations. To appear in Studia Math. (2021). [Google Scholar]
  6. J.-M. Coron, Vol. 136 of Control and nonlinearity. Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2007). [Google Scholar]
  7. M. Egidi and I. Veselić, Sharp geometric condition for null-controllability of the heat equation on ℝd and consistent estimates on the control cost. Arch. Math. (Basel) 111 (2018) 85–99. [CrossRef] [MathSciNet] [Google Scholar]
  8. K.-J. Engel and R. Nagel, One-parameter semigroups for linear evolution equations. Vol 194 of Graduate Texts in Mathematics. Springer-Verlag, New York (2000). [Google Scholar]
  9. S. Huang, G. Wang and M. Wang, Characterizations of stabilizable sets for some parabolic equations in ℝn. J. Differ. Equ. 272 (2021) 255–288. [CrossRef] [Google Scholar]
  10. B. Jaye and M. Mitkovski, Quantitative uniqueness property for L2 functions with fast decaying, or sparsely supported, Fourier transform. Int. Math. Res. Not. (2021) rnab075, https://doi.org/10.1093/imrn/rnab075. [Google Scholar]
  11. A. Koenig, Lack of null-controllability for the fractional heat equation and related equations. SIAM J. Control Optim. 58 (2020) 3130–3160. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Koenig, Contrôlabilité de quelques équations aux dérivées partielles paraboliques peu diffusives. Ph.D thesis, University Côte d’Azur, France (2019). [Google Scholar]
  13. P. Koosis, The Logarithmic Integral I. Cambridge University Press, 1988. [CrossRef] [Google Scholar]
  14. O. Kovrijkine, Some results related to the Logvinenko-Sereda theorem. Proc. Amer. Math. Soc. 129 (2001) 3037–3047. [CrossRef] [MathSciNet] [Google Scholar]
  15. G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur. Comm. Partial Differ. Equ. 20 (1995) 335–356. [CrossRef] [Google Scholar]
  16. P. Lissy, A non-controllability result for the half-heat equation on the whole line based on the prolate spheroidal wave functions and its application to the Grushin equation. Preprint arXiv e-print (2020). [Google Scholar]
  17. H. Liu, G. Wang, Y. Xu and H. Yu, Characterizations on complete stabilizability. Preprint arXiv e-print (2020). [Google Scholar]
  18. J. Martin and K. Pravda-Starov, Geometric conditions for the exact controllability of fractional free and harmonic Schrödinger equations. J. Evol. Equ. 21 (2021) 1059–1087. [CrossRef] [MathSciNet] [Google Scholar]
  19. L. Miller, A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups. Discrete Contin. Dyn. Syst. Ser. B 14 (2010) 1465–1485. [Google Scholar]
  20. F. Nazarov, M. Sodin and A. Volberg, Lower bounds for quasianalytic functions, I. How to control smooth functions. Math. Scand. 95 (2004) 59–79. [CrossRef] [MathSciNet] [Google Scholar]
  21. E. Trélat, G. Wang and Y. Xu, Characterization by observability inequalities of controllability and stabilization properties. Pure Appl. Anal. 2 (2020) 93–122. [CrossRef] [MathSciNet] [Google Scholar]
  22. G. Wang, M. Wang, C. Zhang and Y. Zhang, Observable set, observability, interpolation inequality and spectral inequality for the heat equation in ℝn. J. Math. Pures Appl. 126 (2019) 144–194. [Google Scholar]
  23. S. Xiang, Quantitative rapid and finite time stabilization of the heat equation. Preprint arXiv e-print (2020). [Google Scholar]

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