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All issues Volume 27 (2021) Supplement ESAIM: COCV, 27 (2021) S21 References
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Issue
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S21
Number of page(s) 41
DOI https://doi.org/10.1051/cocv/2020066
Published online 01 March 2021
  1. R.A. Adams, Sobolev Spaces. Vol. 65 of Pure and Applied Mathematics. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1975). [Google Scholar]
  2. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Control Optim. 30 (1992) 1024–1065. [Google Scholar]
  3. J.L. Bona, S.M. Sun and B.-Y, Zhang, A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. Comm. Partial Differential Equations 28 (2003) 1391–1436. [Google Scholar]
  4. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011). [Google Scholar]
  5. E. Cerpa, Exact controllability of a nonlinear Korteweg-de Vries equation on a critical spatial domain. SIAM J. Control Optim. 46 (2007) 877–899. [Google Scholar]
  6. E. Cerpa, Control of a Korteweg-de Vries equation: a tutorial. Math. Control Relat. Fields 4 (2014) 45–99. [Google Scholar]
  7. E. Cerpa and E. Crépeau, Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain. Ann. Inst. Henri Poincaré Anal. Non Linéaire 26 (2009) 457–475. [CrossRef] [Google Scholar]
  8. S.N. Chandler-Wilde, D.P. Hewett and A. Moiola, Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples. Mathematika 61 (2015) 414–443. [CrossRef] [Google Scholar]
  9. F.W. Chaves-Silva and G. Lebeau, Spectral inequality and optimal cost of controllability for the Stokes system. ESAIM: COCV 22 (2016) 1137–1162. [CrossRef] [EDP Sciences] [Google Scholar]
  10. J. Chu, J.-M. Coron and P. Shang, Asymptotic stability of a nonlinear Korteweg–de Vries equation with critical lengths. J. Differential Equations 259 (2015) 4045–4085. [Google Scholar]
  11. J.-M. Coron, Control and, Vol. 136. Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2007). [Google Scholar]
  12. J.-M. Coron and E. Crépeau, Exact boundary controllability of a nonlinear KdV equation with critical lengths. J. Eur. Math. Soc. (JEMS) 6 (2004) 367–398. [CrossRef] [MathSciNet] [Google Scholar]
  13. J.-M. Coron and Q. Lü, Local rapid stabilization for a Korteweg-de Vries equation with a Neumann boundary control on the right. J. Math. Pures Appl. 102 (2014) 1080–1120. [Google Scholar]
  14. J.-M. Coron and H.-M. Nguyen, Null controllability and finite time stabilization for the heat equations with variable coefficients in space in one dimension via backstepping approach. Arch. Ration. Mech. Anal. 225 (2017) 993–1023. [Google Scholar]
  15. J.-M. Coron and L. Praly, Adding an integrator for the stabilization problem. Systems Control Lett. 17 (1991) 89–104. [Google Scholar]
  16. J.-M. Coron, I. Rivas and S. Xiang, Local exponential stabilization for a class of Korteweg–de Vries equations by means of time-varying feedback laws. Anal. Partial Differ. Equ. 10 (2017) 1089–1122. [Google Scholar]
  17. J.-M. Coron and S. Xiang, Small-time global stabilization of the viscous Burgers equation with three scalar controls. Preprint, hal-01723188 (2018). [Google Scholar]
  18. S. Ervedoza and E. Zuazua, Sharp observability estimates for heat equations. Arch. Ration. Mech. Anal. 202 (2011) 975–1017. [Google Scholar]
  19. A.V. Fursikov and O.Y. Imanuvilov, Controllability of Evolution Equations, Vol. 34. Lecture Notes Series. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
  20. M. Krstic and A. Smyshlyaev, Boundary Control of PDEs. A course on backstepping designs, Vol. 16. Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2008). [Google Scholar]
  21. G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur. Comm. Partial Differential Equations 20 (1995) 335–356. [Google Scholar]
  22. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 2, Perturbations. [Perturbations]. Vol. 9. Recherches en Mathématiques Appliquées [Research in Applied Mathematics]. Masson, Paris (1988). [Google Scholar]
  23. P. Lissy, On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension. SIAM J. Control Optim. 52 (2014) 2651–2676. [Google Scholar]
  24. G.A. Perla Menzala, C.F. Vasconcellos and E. Zuazua, Stabilization of the Korteweg-de Vries Equation with localized damping. Q. Appl. Math. LX (2002) 111–129. [Google Scholar]
  25. L. Rosier, Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain. ESAIM: COCV 2 (1997) 33–55. [CrossRef] [EDP Sciences] [Google Scholar]
  26. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton Mathematical Series, Vol. 30. Princeton University Press, Princeton, N.J. (1970). [Google Scholar]
  27. M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups. Birkhäuser Advanced Texts: Basler Lehrbücher. Birkhäuser Advanced Texts: Basel Textbooks. Birkhäuser Verlag, Basel (2009). [Google Scholar]
  28. S. Xiang, Small-time local stabilization for a Korteweg-de Vries equation. Syst. Control Lett. 111 (2018) 64–69. [Google Scholar]
  29. S. Xiang, Null controllability of a linearized Korteweg-de Vries equation by backstepping approach. SIAM J. Control Optim. 57 (2019) 1493–1515. [Google Scholar]
  30. C. Zhang, Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback. Preprint arXiv:1810.11214 (2019). [Google Scholar]
  31. C. Zhang, Finite-time internal stabilization of a linear 1-D transport equation. Systems Control Lett. 133 (2019) 104529. [Google Scholar]

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