On the Controllability of the Fifth-Order Korteweg-De Vries Equation
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2181-2209.
@article{AIHPC_2009__26_6_2181_0,
     author = {Glass, O. and Guerrero, S.},
     title = {On the {Controllability} of the {Fifth-Order} {Korteweg-De} {Vries} {Equation}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2181--2209},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.01.010},
     mrnumber = {2569891},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.010/}
}
TY  - JOUR
AU  - Glass, O.
AU  - Guerrero, S.
TI  - On the Controllability of the Fifth-Order Korteweg-De Vries Equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 2181
EP  - 2209
VL  - 26
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.010/
DO  - 10.1016/j.anihpc.2009.01.010
LA  - en
ID  - AIHPC_2009__26_6_2181_0
ER  - 
%0 Journal Article
%A Glass, O.
%A Guerrero, S.
%T On the Controllability of the Fifth-Order Korteweg-De Vries Equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2181-2209
%V 26
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.010/
%R 10.1016/j.anihpc.2009.01.010
%G en
%F AIHPC_2009__26_6_2181_0
Glass, O.; Guerrero, S. On the Controllability of the Fifth-Order Korteweg-De Vries Equation. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2181-2209. doi : 10.1016/j.anihpc.2009.01.010. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.010/

[1] Bona J., 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 | Zbl

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

[3] Cerpa E., Crépeau E., Boundary Controllability for the Nonlinear Korteweg-De Vries Equation on Any Critical Domain, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2) (2009) 457-475. | Numdam | MR | Zbl

[4] Colin T., Ghidaglia J.-M., An Initial-Boundary Value Problem for the Korteweg-De Vries Equation Posed on a Finite Interval, Adv. Differential Equations 6 (12) (2001) 1463-1492. | MR | Zbl

[5] Colliander J. E., Kenig C. E., The Generalized Korteweg-De Vries Equation on the Half Line, Comm. Partial Differential Equations 27 (11-12) (2002) 2187-2266. | MR | Zbl

[6] Coron J.-M., Crépeau E., Exact Boundary Controllability of a Nonlinear KdV Equation With Critical Lengths, J. Eur. Math. Soc. 6 (2004) 367-398. | MR | Zbl

[7] Coron J.-M., Control and Nonlinearity, Math. Surveys Monogr., vol. 136, Amer. Math. Soc., Providence, RI, 2007. | MR | Zbl

[8] Cui S. B., Deng D. G., Tao S. P., Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation With L 2 Initial Data, Acta Math. Sin. (Engl. Ser.) 22 (5) (2006) 1457-1466. | MR | Zbl

[9] Dawson L., Uniqueness Properties of Higher Order Dispersive Equations, J. Differential Equations 236 (1) (2007) 199-236. | MR | Zbl

[10] Doronin G., Larkin N., Kawahara Equation in a Bounded Domain, Discrete Contin. Dyn. Syst. Ser. B 10 (4) (2008) 783-799. | MR | Zbl

[11] Faminskii A. V., On Two Initial Boundary Value Problems for the Generalized KdV Equation, Nonlinear Bound. Probl. 14 (2004) 58-71. | Zbl

[12] Fursikov A., Imanuvilov O. Yu., Controllability of Evolution Equations, Lecture Notes Ser., vol. 34, Seoul National University, Korea, 1996. | MR | Zbl

[13] Glass O., Guerrero S., Some Exact Controllability Results for the Linear KdV Equation and Uniform Controllability in the Zero-Dispersion Limit, Asymptot. Anal. 60 (1-2) (2008) 61-100. | MR | Zbl

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

[15] Kawahara R., Oscillatory Solitary Waves in Dispersive Media, J. Phys. Soc. Japan 33 (1972) 260-264.

[16] Kenig C., Ponce G., Vega L., Higher-Order Nonlinear Dispersive Equations, Proc. Amer. Math. Soc. 122 (1) (1994) 157-166. | MR | Zbl

[17] Kichenassamy S., Olver P. J., Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations, SIAM J. Math. Anal. 23 (5) (1992) 1141-1166. | MR | Zbl

[18] Kwon S., Well-Posedness and Ill-Posedness of the Fifth-Order Modified KdV Equation, Electron. J. Differential Equations 2008 (01) (2008) 1-15. | MR | Zbl

[19] Olver P. J., Hamiltonian and Non-Hamiltonian Models for Water Waves, in: Ciarlet P. G., Roseau M. (Eds.), Trends and Applications of Pure Mathematics to Mechanics, Lecture Notes in Phys., vol. 195, Springer-Verlag, New York, 1984, pp. 273-290. | MR | Zbl

[20] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci., vol. 44, Springer-Verlag, New York, 1983. | MR | Zbl

[21] Ponce G., Lax Pairs and Higher Order Models for Water Waves, J. Differential Equations 102 (2) (1993) 360-381. | MR | Zbl

[22] Rosier L., Exact Boundary Controllability for the Korteweg-De Vries Equation on a Bounded Domain, ESAIM Control Optim. Calc. Var. 2 (1997) 33-55. | Numdam | MR | Zbl

[23] 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. | MR | Zbl

[24] Rosier L., Control of the Surface of a Fluid by a Wavemaker, ESAIM Control Optim. Calc. Var. 10 (3) (2004) 346-380. | Numdam | MR | Zbl

[25] Russell D. L., Zhang B. Y., Controllability and Stabilizability of the Third-Order Linear Dispersion Equation on a Periodic Domain, SIAM J. Control Optim. 31 (3) (1993) 659-676. | MR | Zbl

[26] 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 | Zbl

Cité par Sources :