Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
ESAIM: Control, Optimisation and Calculus of Variations, Volume 2  (1997), p. 33-55
@article{COCV_1997__2__33_0,
     author = {Rosier, Lionel},
     title = {Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {2},
     year = {1997},
     pages = {33-55},
     zbl = {0873.93008},
     mrnumber = {1440078},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1997__2__33_0}
}
Rosier, Lionel. Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain. ESAIM: Control, Optimisation and Calculus of Variations, Volume 2 (1997) , pp. 33-55. http://www.numdam.org/item/COCV_1997__2__33_0/

[1] 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. | MR 1178650 | Zbl 0786.93009

[2] J. Bona and R. Winther: The Korteweg-de Vries equation, posed in a quarter-plane, SIAM J. Math Anal., 14, 1983, 1056-1106. | MR 718811 | Zbl 0529.35069

[3] J.M. Coron: Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris, t. 317, Série I, 1993, 271-276. | MR 1233425 | Zbl 0781.76013

[4] A.V. Fursikov and O. Y. Imanuvilov: On controllability of certain systems simulating a fluid flow, in Flow Control, IMA, Math. Appl., vol. 68, Gunzberger ed., Springer-Verlag, New York, 1995, 148-184. | MR 1348646 | Zbl 0922.93006

[5] L.F. Ho: Observabilité frontière de l'équation des ondes, C. R. Acad. Sci. Paris, Série 1 Math., 302, 1986, 443-446. | MR 838598 | Zbl 0598.35060

[6] A.E. Ingham: Some trigonometrical inequalities with application to the theory of series, Math. A., 41, 1936, 367-379. | MR 1545625 | Zbl 0014.21503

[7] V. Komornik: Exact controllability and stabilization, the multiplier method, R.A.M. 36, John Wiley-Masson, 1994. | MR 1359765 | Zbl 0937.93003

[8] V. Komornik, D.L. Russel and B.-Y. Zhang: Control and stabilization of the Korteweg-de Vries equation on a periodic domain, submitted to J. Differential Equations.

[9] D.J. Korteweg and G. De Vries: On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag., 5, 39, 1895, 422-423. | JFM 26.0881.02

[10] G. Lebeau: Contrôle de l'équation de Schrödinger, J. Math. Pures Appl., 71, 1992, 267-291. | MR 1172452 | Zbl 0838.35013

[11] J.L. Lions: Contrôlabilité exacte de systèmes distribués, C.R. Acad. Sci. Paris, 302, 1986, 471-475. | MR 838402 | Zbl 0589.49022

[12] J.L. Lions: Contrôlabilité exacte, Perturbations et Stabilisation de Systèmes Distribués, Tome 1, Contrôlabilité exacte, Collection de recherche en mathématiques appliquées, 8, Masson, Paris, 1988. | MR 953547 | Zbl 0653.93002

[13] J.L. Lions: Exact controllability, stabilizability, and perturbations for distributed systems, Siam Rev., 30, 1988, 1-68. | MR 931277 | Zbl 0644.49028

[14] E. Machtyngier: Exact controllability for the Schrödinger equation, SIAM J. Control Optim., 32, 1994, 24-34. | MR 1255957 | Zbl 0795.93018

[15] A. Pazy: Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983. | MR 710486 | Zbl 0516.47023

[16] D.L. Russel and B-Y. Zhang: Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain, SIAM J. Control Optim., 31, 1993, 659-673. | MR 1214759 | Zbl 0771.93073

[17] J.C. Saut and R. Temam: Remarks on the Korteweg-De Vries equation, Israel. Math., 24, 1976, 78-87. | MR 454425 | Zbl 0334.35062

[18] J. Simon: Compact sets in the space Lp(0,T, B), Annali di Matematica pura ed applicata (IV), vol. CXLVI, 1987, 65-96. | MR 916688 | Zbl 0629.46031

[19] K. Yosida: Functional Analysis, Springer-Verlag, Berlin Heidelberg New York, 1978. | MR 500055 | Zbl 0365.46001

[20] B.-Y. Zhang: Some results for nonlinear dispersive wave equations with applications to control, Ph. D. thesis, University of Wisconsin, Madison, June 1990.