EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 10 / No 3 (July 2004) ESAIM: COCV, 10 3 (2004) 346-380 References
Free Access
Issue
ESAIM: COCV
Volume 10, Number 3, July 2004
Page(s) 346 - 380
DOI https://doi.org/10.1051/cocv:2004012
Published online 15 June 2004
  1. S.N. Antontsev, A.V. Kazhikov and V.N. Monakhov, Boundary values problems in mechanics of nonhomogeneous fluids. North-Holland, Amsterdam (1990). [Google Scholar]
  2. P. Benilan and R. Gariepy, Strong solutions in L1 of degenerate parabolic equations. J. Differ. Equations 119 (1995) 473-502. [CrossRef] [Google Scholar]
  3. J.L. Bona, M. Chen and J.-C. Saut, Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory. J. Nonlinear Sci. 12 (2002) 283-318. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.L. Bona, S. Sun and B.-Y. Zhang, A Non-homogeneous Boundary-Value Problem for the Korteweg-de Vries Equation Posed on a Finite Domain. Commun. Partial Differ. Equations 28 (2003) 1391-1436. [CrossRef] [Google Scholar]
  5. J.L. Bona and R. Winther, The Korteweg-de Vries equation, posed in a quarter-plane. SIAM J. Math. Anal. 14 (1983) 1056-1106. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.-M. Coron, On the controllability of the 2-D incompressible perfect fluids. J. Math. Pures Appl. 75 (1996) 155-188. [Google Scholar]
  7. J.-M. Coron, Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, A tribute to J.L. Lions. ESAIM: COCV 8 (2002) 513-554. [CrossRef] [EDP Sciences] [Google Scholar]
  8. E. Crépeau, Exact boundary controllability of the Korteweg-de Vries equation around a non-trivial stationary solution. Int. J. Control 74 (2001) 1096-1106. [CrossRef] [Google Scholar]
  9. E. Fernández-Cara, Null controllability of the semilinear heat equation. ESAIM: COCV 2 (1997) 87-103. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  10. A.V. Fursikov and O.Y. Imanuvilov, On controllability of certain systems simulating a fluid flow, in Flow Control, M.D. Gunzburger Ed., Springer-Verlag, New York, IMA Vol. Math. Appl. 68 (1995) 149-184. [Google Scholar]
  11. T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equations. Stud. App. Math. 8 (1983) 93-128. [Google Scholar]
  12. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes, Vol. 1. Dunod, Paris (1968). [Google Scholar]
  13. G. Mathieu-Girard, Étude et contrôle des équations de la théorie “Shallow water” en dimension un. Ph.D. thesis, Université Paul Sabatier, Toulouse III (1998). [Google Scholar]
  14. S. Micu, On the controllability of the linearized Benjamin-Bona-Mahony equation. SIAM J. Control Optim. 39 (2001) 1677-1696. [CrossRef] [MathSciNet] [Google Scholar]
  15. S. Micu and J.H. Ortega, On the controllability of a linear coupled system of Korteweg-de Vries equations. Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000). Philadelphia, PA SIAM (2000) 1020-1024. [Google Scholar]
  16. S. Mottelet, Controllability and stabilization of a canal with wave generators. SIAM J. Control Optim. 38 (2000) 711-735. [CrossRef] [MathSciNet] [Google Scholar]
  17. S. Mottelet, Controllability and stabilization of liquid vibration in a container during transportation. (Preprint.) [Google Scholar]
  18. N. Petit and P. Rouchon, Dynamics and solutions to some control problems for water-tank systems. IEEE Trans. Automat. Control 47 (2002) 594-609. [CrossRef] [MathSciNet] [Google Scholar]
  19. L. Rosier, Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain. ESAIM: COCV 2 (1997) 33-55, http://www.edpsciences.org/cocv [CrossRef] [EDP Sciences] [Google Scholar]
  20. L. Rosier, Exact boundary controllability for the linear Korteweg-de Vries equation – a numerical study. ESAIM Proc. 4 (1998) 255-267, http://www.edpsciences.org/proc [CrossRef] [Google Scholar]
  21. L. Rosier, Exact boundary controllability for the linear Korteweg-de Vries equation on the half-line. SIAM J. Control Optim. 39 (2000) 331-351. [CrossRef] [MathSciNet] [Google Scholar]
  22. D.L. Russell 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. [CrossRef] [MathSciNet] [Google Scholar]
  23. D.L. Russell and B.-Y. Zhang, Exact controllability and stabilizability of the Korteweg-de Vries equation. Trans. Amer. Math. Soc. 348 (1996) 3643-3672. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Simon, Compact Sets in the Space Formula . Ann. Mat. Pura Appl. (IV) CXLVI (1987) 65-96. [Google Scholar]
  25. G.B. Whitham, Linear and nonlinear waves. A Wiley-Interscience publication, Wiley, New York (1999) reprint of the 1974 original. [Google Scholar]
  26. E. Zeidler, Nonlinear functional analysis and its applications, Part 1. Springer-Verlag, New York (1986). [Google Scholar]
  27. B.-Y. Zhang, Exact boundary controllability of the Korteweg-de Vries equation. SIAM J. Control Optim. 37 (1999) 543-565. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.