EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 17 / No 1 (January-March 2011) ESAIM: COCV, 17 1 (2011) 102-116 References
Free Access
Issue
ESAIM: COCV
Volume 17, Number 1, January-March 2011
Page(s) 102 - 116
DOI https://doi.org/10.1051/cocv/2009041
Published online 30 October 2009
  1. T.B. Benjamin, J.L. Bona and J.J. Mahony, Model equations for long waves in nonlinear dispersive systems. Phil. Trans. R. Soc. A 272 (1972) 47–78. [Google Scholar]
  2. N.G. Berloff and L.N. Howard, Solitary and periodic solutions for nonlinear nonintegrable equations. Stud. Appl. Math. 99 (1997) 1–24. [CrossRef] [MathSciNet] [Google Scholar]
  3. H.A. Biagioni and F. Linares, On the Benney-Lin and Kawahara equations. J. Math. Anal. Appl. 211 (1997) 131–152. [CrossRef] [MathSciNet] [Google Scholar]
  4. J.L. Bona and H. Chen, Comparison of model equations for small-amplitude long waves. Nonlinear Anal. 38 (1999) 625–647. [CrossRef] [MathSciNet] [Google Scholar]
  5. T.J. Bridges and G. Derks, Linear instability of solitary wave solutions of the Kawahara equation and its generalizations. SIAM J. Math. Anal. 33 (2002) 1356–1378. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.M. Coron and E. Crépeau, Exact boundary controllability of a nonlinear KdV equation with critical lenghts. J. Eur. Math. Soc. 6 (2004) 367–398. [Google Scholar]
  7. G.G. Doronin and N.A. Larkin, Kawahara equation in a bounded domain. Discrete Continuous Dyn. Syst., Ser. B 10 (2008) 783–799. [Google Scholar]
  8. H. Hasimoto, Water waves. Kagaku 40 (1970) 401–408 [in Japanese]. [Google Scholar]
  9. T. Kakutani and H. Ono, Weak non-linear hydromagnetic waves in a cold collision-free plasma. J. Phys. Soc. Japan 26 (1969) 1305–1318. [Google Scholar]
  10. T. Kawahara, Oscillatory solitary waves in dispersive media. J. Phys. Soc. Japan 33 (1972) 260–264. [Google Scholar]
  11. F. Linares and J.H. Ortega, On the controllability and stabilization of the linearized Benjamin-Ono equation. ESAIM: COCV 11 (2005) 204–218. [CrossRef] [EDP Sciences] [Google Scholar]
  12. F. Linares and A.F. Pazoto, On the exponential decay of the critical generalized Korteweg-de Vries with localized damping. Proc. Amer. Math. Soc. 135 (2007) 1515–1522. [CrossRef] [MathSciNet] [Google Scholar]
  13. J.L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Tome 1: Contrôlabilité Exacte, in RMA 8, Masson, Paris, France (1988). [Google Scholar]
  14. C.P. Massarolo, G.P. Menzala and A.F. Pazoto, On the uniform decay for the Korteweg-de Vries equation with weak damping. Math. Meth. Appl. Sci. 30 (2007) 1419–1435. [Google Scholar]
  15. G.P. Menzala, C.F. Vasconcellos and E. Zuazua, Stabilization of the Korteweg-de Vries equation with localized damping. Quarterly Applied Math. LX (2002) 111–129. [Google Scholar]
  16. A.F. Pazoto, Unique continuation and decay for the Korteweg-de Vries equation with localized damping. ESAIM: COCV 11 (2005) 473–486. [CrossRef] [EDP Sciences] [Google Scholar]
  17. A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York, USA (1983). [Google Scholar]
  18. J. Rauch and M. Taylor, Exponential decay of solutions to hyperbolic equations in bounded domains. Indiana Univ. Math. J. 24 (1974) 79–86. [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. [CrossRef] [EDP Sciences] [Google Scholar]
  20. L. Rosier and B.Y. Zhang, Global stabilization of the generalized Korteweg-de Vries equation posed on a finite domain. SIAM J. Contr. Opt. 45 (2006) 927–956. [Google Scholar]
  21. D.L. Russell and B.Y. Zhang, Exact controllability and stabilization of the Korteweg-de Vries equation. Trans. Amer. Math. Soc. 348 (1996) 1515–1522. [Google Scholar]
  22. J.C. Saut and B. Scheurer, Unique continuation for some evolution equations. J. Diff. Equation 66 (1987) 118–139. [Google Scholar]
  23. G. Schneider and C.E. Wayne, The rigorous approximation of long-wavelength capillary-gravity waves. Arch. Ration. Mech. Anal. 162 (2002) 247–285. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Topper and T. Kawahara, Approximate equations for long nonlinear waves on a viscous fluid. J. Phys. Soc. Japan 44 (1978) 663–666. [CrossRef] [MathSciNet] [Google Scholar]
  25. C.F. Vasconcellos and P.N. da Silva, Stabilization of the linear Kawahara equation with localized damping. Asymptotic Anal. 58 (2008) 229–252. [Google Scholar]
  26. C.F. Vasconcellos and P.N. da Silva, Erratum of the Stabilization of the linear Kawahara equation with localized damping. Asymptotic Anal. (to appear). [Google Scholar]
  27. E. Zuazua, Contrôlabilité Exacte de Quelques Modèles de Plaques en un Temps Arbitrairement Petit. Appendix in [13], 165–191. [Google Scholar]
  28. E. Zuazua, Exponential decay for the semilinear wave equation with locally distribued damping. Comm. Partial Diff. Eq. 15 (1990) 205–235. [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.