@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}, pages = {33--55}, publisher = {EDP-Sciences}, volume = {2}, year = {1997}, mrnumber = {1440078}, zbl = {0873.93008}, language = {en}, url = {http://www.numdam.org/item/COCV_1997__2__33_0/} }
TY - JOUR AU - Rosier, Lionel TI - Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1997 SP - 33 EP - 55 VL - 2 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_1997__2__33_0/ LA - en ID - COCV_1997__2__33_0 ER -
%0 Journal Article %A Rosier, Lionel %T Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain %J ESAIM: Control, Optimisation and Calculus of Variations %D 1997 %P 33-55 %V 2 %I EDP-Sciences %U http://www.numdam.org/item/COCV_1997__2__33_0/ %G en %F 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, Tome 2 (1997), pp. 33-55. http://www.numdam.org/item/COCV_1997__2__33_0/
[1] Sharp sufficient conditions for the observation, control and stabilization of waves from the boundary, SIAM J. Control Optim., 30, 1992, 1024-1065. | MR | Zbl
, and :[2] The Korteweg-de Vries equation, posed in a quarter-plane, SIAM J. Math Anal., 14, 1983, 1056-1106. | MR | Zbl
and :[3] 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 | Zbl
:[4] 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 | Zbl
and :[5] Observabilité frontière de l'équation des ondes, C. R. Acad. Sci. Paris, Série 1 Math., 302, 1986, 443-446. | MR | Zbl
:[6] Some trigonometrical inequalities with application to the theory of series, Math. A., 41, 1936, 367-379. | EuDML | MR | Zbl
:[7] Exact controllability and stabilization, the multiplier method, R.A.M. 36, John Wiley-Masson, 1994. | MR | Zbl
:[8] Control and stabilization of the Korteweg-de Vries equation on a periodic domain, submitted to J. Differential Equations.
, and :[9] 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
and :[10] Contrôle de l'équation de Schrödinger, J. Math. Pures Appl., 71, 1992, 267-291. | MR | Zbl
:[11] Contrôlabilité exacte de systèmes distribués, C.R. Acad. Sci. Paris, 302, 1986, 471-475. | MR | Zbl
:[12] Contrôlabilité exacte, Perturbations et Stabilisation de Systèmes Distribués, Tome 1, Contrôlabilité exacte, Collection de recherche en mathématiques appliquées, 8, Masson, Paris, 1988. | MR | Zbl
:[13] Exact controllability, stabilizability, and perturbations for distributed systems, Siam Rev., 30, 1988, 1-68. | MR | Zbl
:[14] Exact controllability for the Schrödinger equation, SIAM J. Control Optim., 32, 1994, 24-34. | MR | Zbl
:[15] Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New York, 1983. | MR | Zbl
:[16] Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain, SIAM J. Control Optim., 31, 1993, 659-673. | MR | Zbl
and :[17] Remarks on the Korteweg-De Vries equation, Israel. Math., 24, 1976, 78-87. | MR | Zbl
and :[18] Compact sets in the space Lp(0,T, B), Annali di Matematica pura ed applicata (IV), vol. CXLVI, 1987, 65-96. | MR | Zbl
:[19] Functional Analysis, Springer-Verlag, Berlin Heidelberg New York, 1978. | MR | Zbl
:[20] Some results for nonlinear dispersive wave equations with applications to control, Ph. D. thesis, University of Wisconsin, Madison, June 1990.
: