Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 48
Number of page(s) 36
DOI https://doi.org/10.1051/cocv/2023016
Published online 21 June 2023
  1. F. Alabau-Boussouira, P. Cannarsa and F. Fragnelli, Carleman estimates for degenerate parabolic operators with applications to null controllability. J. Evol. Equ. 6 (2006) 161–204. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Alessandrini and L. Escauriaza, Null-controllability of one-dimensional parabolic equations. ESAIM Control Optim. Calc. Var. 14 (2008) 284–293. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  3. F.V. Atkinson and C.T. Fulton, Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit-circle singularity. I. Proc. Roy. Soc. Edinburgh Sect. A 99 (1984) 51–70. [CrossRef] [MathSciNet] [Google Scholar]
  4. K. Beauchard, P. Cannarsa and R. Guglielmi, Null controllability of Grushin-type operators in dimension two. J. Eur. Math. Soc. (JEMS) 16 (2014) 67–101. [CrossRef] [MathSciNet] [Google Scholar]
  5. K. Beauchard, J. Dardé and S. Ervedoza, minimal time issues for the observability of Grushin-type equations. Ann. Inst. Fourier (Grenoble) 70 (2020) 247–312. [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Birkhoff and G.-C. Rota, Ordinary Differential Equations, Ginn-Blaisdell, Boston (1962). [Google Scholar]
  7. J.S. Bradley, Hardy inequalities with mixed norms. Canad. Math. Bull. 21 (1978) 405–408. [CrossRef] [MathSciNet] [Google Scholar]
  8. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext. Springer, New York (2011). [CrossRef] [Google Scholar]
  9. P. Cannarsa, P. Martinez and J. Vancostenoble, Carleman estimates for a class of degenerate parabolic operators. SIAM J. Control Optim. 47 (2008) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Cannarsa, P. Martinez and J. Vancostenoble, Global Carleman estimates for degenerate parabolic operators with applications. Mem. Amer. Math. Soc. 239 (2016) 209. [Google Scholar]
  11. P. Cannarsa, P. Martinez and J. Vancostenoble, The cost of controlling strongly degenerate parabolic equations. ESAIM Control Optim. Calc. Var. 26 (2020) 50. [CrossRef] [EDP Sciences] [Google Scholar]
  12. D.M. Duc, A class of strongly degenerate elliptic operators, Bull. Austral. Math. Soc. 39 (1989) 177–200. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Fragnelli and D. Mugnai, Carleman estimates, observability inequalities and null controllability for interior degenerate nonsmooth parabolic equations. Mem. Amer. Math. Soc. 242 (2016) 84. [Google Scholar]
  14. G. Fragnelli and D. Mugnai, Singular parabolic equations with interior degeneracy and non smooth coefficients: the Neumann case. Discrete Contin. Dyn. Syst. Ser. S 13 (2020) 1495–1511. [MathSciNet] [Google Scholar]
  15. G. Fragnelli and D. Mugnai, Control of Degenerate and Singular Equations – Carleman Estimates and Observability, SpringerBriefs in Mathematics, BCAM SpringerBriefs, Springer, Cham (2021). [CrossRef] [Google Scholar]
  16. G. Hardy, J.E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, Cambridge (1952). [Google Scholar]
  17. B.J. Harris, Asymptotics of eigenvalues for regular Sturm-Liouville problems. J. Math. Anal. Appl. 183 (1994) 25–36. [CrossRef] [MathSciNet] [Google Scholar]
  18. B.J. Harris and D. Race, Asymptotics for Sturm-Liouville problems with an interior singularity. J. Diff. Equ. 116 (1995) 88–118. [CrossRef] [Google Scholar]
  19. B. Laroche, P. Martin and P. Rouchon, Motion planning for the heat equation. Int. J. Robust Nonlinear Control 10 (2000) 629–643. [CrossRef] [Google Scholar]
  20. C. Laurent and L. Rosier, Exact controllability of semilinear heat equations in spaces of analytic functions. Ann. Inst. H. Poincaré C. Anal. Non Linéaire 37 (2020) 1047–1073. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Martin, I. Rivas, L. Rosier and P. Rouchon, Exact controllability of a linear Korteweg-de Vries equation by the flatness approach. SIAM J. Control Optim. 57 (2019) 2467–2486. [CrossRef] [MathSciNet] [Google Scholar]
  22. P. Martin, L. Rosier and P. Rouchon, Null controllability of the heat equation using flatness. Automatica 50 (2014) 3067–3076. [CrossRef] [MathSciNet] [Google Scholar]
  23. P. Martin, L. Rosier and P. Rouchon, On the reachable states for the boundary control of the heat equation. Appl. Math. Res. Express. (2016) 181–216. [CrossRef] [Google Scholar]
  24. P. Martin, L. Rosier and P. Rouchon, Null controllability of one-dimensional parabolic equations by the flatness approach. SIAM J. Control Optim. 54 (2016) 198–220. [CrossRef] [MathSciNet] [Google Scholar]
  25. P. Martin, L. Rosier and P. Rouchon, Controllability of the 1D Schrödinger equation using flatness. Automatica 91 (2018) 208–216. [CrossRef] [Google Scholar]
  26. I. Moyano, Flatness for a strongly degenerate 1-D parabolic equation. Math. Control Signals Syst. 28 (2016) 22. [CrossRef] [Google Scholar]
  27. B. Muckenhoupt, Hardy’s inequality with weights. Studia Math. 44 (1972) 31–38. [CrossRef] [MathSciNet] [Google Scholar]
  28. N.S. Trudinger, Linear elliptic operators with measurable coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27 (1973) 265–308. [MathSciNet] [Google Scholar]
  29. W. Walter, Ordinary Differential Equations, Graduate Texts in Mathematics, 182. Readings in Mathematics, Springer-Verlag, New York, 1998. [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.