Boundary Controllability for the Nonlinear Korteweg-De Vries Equation on Any Critical Domain
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 2, p. 457-475
@article{AIHPC_2009__26_2_457_0,
     author = {Cerpa, Eduardo and Cr\'ePeau, Emmanuelle},
     title = {Boundary Controllability for the Nonlinear Korteweg-De Vries Equation on Any Critical Domain},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {26},
     number = {2},
     year = {2009},
     pages = {457-475},
     doi = {10.1016/j.anihpc.2007.11.003},
     zbl = {1158.93006},
     mrnumber = {2504039},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2009__26_2_457_0}
}
Cerpa, Eduardo; CréPeau, Emmanuelle. Boundary Controllability for the Nonlinear Korteweg-De Vries Equation on Any Critical Domain. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 2, pp. 457-475. doi : 10.1016/j.anihpc.2007.11.003. http://www.numdam.org/item/AIHPC_2009__26_2_457_0/

[1] Beauchard K., Local Controllability of a 1-D Schrödinger Equation, J. Math. Pures Appl. (9) 84 (7) (2005) 851-956, MR MR2144647. | MR 2144647 | Zbl 1124.93009

[2] Beauchard K., Coron J.-M., Controllability of a Quantum Particle in a Moving Potential Well, J. Funct. Anal. 232 (2) (2006) 328-389, MR MR2200740. | MR 2200740 | Zbl pre05017416

[3] Bona J. L., Sun S. M., Zhang B.-Y., A Nonhomogeneous Boundary-Value Problem for the Korteweg-De Vries Equation Posed on a Finite Domain, Comm. Partial Differential Equations 28 (7-8) (2003) 1391-1436, MR MR1998942 (2004h:35195). | MR 1998942 | Zbl 1057.35049

[4] Cerpa E., Exact Controllability of a Nonlinear Korteweg-De Vries Equation on a Critical Spatial Domain, SIAM J. Control Optim. 46 (3) (2007) 877-899. | MR 2338431 | Zbl 1147.93005

[5] M. Chapouly, Global controllability of a nonlinear Korteweg-de Vries equation, Preprint, 2007. | MR 2538210 | Zbl 1170.93006

[6] Coron J.-M., Global Asymptotic Stabilization for Controllable Systems Without Drift, Math. Control Signals Systems 5 (3) (1992) 295-312, MR MR1164379 (93m:93084). | MR 1164379 | Zbl 0760.93067

[7] Coron J.-M., On the Controllability of 2-D Incompressible Perfect Fluids, J. Math. Pures Appl. (9) 75 (2) (2007) 155-188, MR MR1380673 (97b:93010). | MR 1380673 | Zbl 0848.76013

[8] Coron J.-M., Local Controllability of a 1-D Tank Containing a Fluid Modeled by the Shallow Water Equations, ESAIM Control Optim. Calc. Var. 8 (2002) 513-554, (electronic). A tribute to J.L. Lions, MR MR1932962 (2004a:93009). | Numdam | MR 1932962 | Zbl 1071.76012

[9] Coron J.-M., On the Small-Time Local Controllability of a Quantum Particle in a Moving One-Dimensional Infinite Square Potential Well, C. R. Math. Acad. Sci. Paris 342 (2) (2006) 103-108, MR MR2193655. | MR 2193655 | Zbl 1082.93002

[10] Coron J.-M., Control and Nonlinearity, Mathematical Surveys and Monographs, vol. 136, American Mathematical Society, Providence, RI, 2007, MR MR2302744. | MR 2302744 | Zbl 1140.93002

[11] Coron J.-M., Crépeau E., Exact Boundary Controllability of a Nonlinear KdV Equation With Critical Lengths, J. Eur. Math. Soc. (JEMS) 6 (3) (2004) 367-398, MR MR2060480 (2005b:93016). | MR 2060480 | Zbl 1061.93054

[12] Coron J.-M., Trélat E., Global Steady-State Controllability of One-Dimensional Semilinear Heat Equations, SIAM J. Control Optim. 43 (2) (2004) 549-569, (electronic), MR MR2086173 (2005f:93009). | MR 2086173 | Zbl 1101.93011

[13] Coron J.-M., Trélat E., Global Steady-State Stabilization and Controllability of 1D Semilinear Wave Equations, Commun. Contemp. Math. 8 (4) (2006) 535-567, MR MR2258876. | MR 2258876 | Zbl 1101.93039

[14] O. Glass, S. Guerrero, Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit, Preprint, Université de Paris 6, 2007. | MR 2463799 | Zbl 1160.35063

[15] Holmer J., The Initial-Boundary Value Problem for the Korteweg-De Vries Equation, Comm. Partial Differential Equations 31 (7-9) (2006) 1151-1190, MR MR2254610. | MR 2254610 | Zbl 1111.35062

[16] Korteweg D. J., De Vries G., On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves, Philos. Mag. 39 (1895) 422-443. | JFM 26.0881.02

[17] Lions J.-L., Contrôlabilité Exacte, Perturbations Et Stabilisation De Systèmes Distribués. Tome 1, Recherches en Mathématiques Appliquées, vol. 8, Masson, Paris, 1988, MR MR953547 (90a:49040). | MR 953547 | Zbl 0653.93002

[18] Rosier L., Exact Boundary Controllability for the Korteweg-De Vries Equation on a Bounded Domain, ESAIM Control Optim. Calc. Var. 2 (1997) 33-55, (electronic), MR MR1440078 (98d:93016). | Numdam | MR 1440078 | Zbl 0873.93008

[19] Rosier L., Exact Boundary Controllability for the Linear Korteweg-De Vries Equation on the Half-Line, SIAM J. Control Optim. 39 (2) (2000) 331-351, (electronic), MR MR1788062 (2001j:93012). | MR 1788062 | Zbl 0966.93055

[20] Rosier L., Control of the Surface of a Fluid by a Wavemaker, ESAIM Control Optim. Calc. Var. 10 (3) (1988) 346-380, (electronic), MR MR2084328 (2005h:93091). | Numdam | MR 2084328 | Zbl 1094.93014

[21] Russell D. L., Zhang B. Y., Exact Controllability and Stabilizability of the Korteweg-De Vries Equation, Trans. Amer. Math. Soc. 348 (9) (1996) 3643-3672, MR MR1360229 (96m:93025). | MR 1360229 | Zbl 0862.93035

[22] Zhang B. Y., Exact Boundary Controllability of the Korteweg-De Vries Equation, SIAM J. Control Optim. 37 (2) (1999) 543-565, (electronic), MR MR1670653 (2000b:93010). | MR 1670653 | Zbl 0930.35160