The generalized Korteweg-de Vries equation on the half line

Communications in Partial Differential Equations

Volumn 27, Issue 11-12, 2002, Pages 2187-2266

  Colliander, J E ^a   Kenig, C E ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036956556     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-120016157     Document Type: Article

References (26)

1. Bona, J.; Sun, S.; Zhang, B.-Y. A Non-Homogeneous Boundary Value Problem for the Korteweg-de Vries Equation in a Quarter-Plane. Preprint, 2000.
2. Bona, J.; Winther, R. The Korteweg-de Vries Equation, Posed in a Quarter-Plane. SIAM J. Math. Anal. 1983, 14(6), 1056-1106.
3. Bona, J.L.; Luo, L. A Generalized Korteweg-de Vries Equation in a Quarter-Plane, Applied Analysis (Baton Rouge, LA, 1996). Amer. Math. Soc. 1999, 59-65.
4. Bona, J.L.; Winther, R. The Korteweg-de Vries Equation in a Quarter-Plane, Continuous Dependence Results. Differential Integral Equations 1989, 2(2), 228-250.
5. Bourgain, J. Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations I, II. Geom. Funct. Anal. 1993, 3, 107-156, 209-262.
6. Calderón, A.P. Boundary Value Problems for Elliptic Equations; Outlines of the Joint Soviet-American Symposium on Partial Differential Equations. Novosibirsk, August 1963; 303-304.
7. Christ, M.; Kiselev, A. Maximal Functions Associated to Filtrations. J. Funct. Anal. 2001, 179, 409-425.
8. Colin, T.; Ghidaglia, J.-M. An Initial-Boundary-Value Problem for the Korteweg-de Vries Equation Posed on a Finite Interval. Advances in Diff. Eqs. 2001, 6, 1463-1492.
9. Faminskiĩ, A.V. A Mixed Problem in a Semistrip for the Korteweg-de Vries Equation and Its Generalizations. Trudy Moskov. Math. Obshch. 1988, 51, 54-94. (English Translation in Trans. Moscow Math. Soc. 1989, 53-91).
10. Faminskiĩ, A.V. Nonlocal Well-Posedness of a Mixed Problem in a Half-Strip for the Korteweg-de Vries Equation. Vestnik RUDN Ser. Mat. 1996, 3, 156-176, (Russian).
11. Faminskiĩ, A.V. Mixed Problems for the Korteweg-de Vries Equation. Sbornik Math. 1999, 190, 903-935.
12. Fibich, G.; Merle, F. Self-Focusing on Bounded Domains. Physica D. 2001, 155(1-2), 132-158.
13. Fokas, A.S.; Sung, L.Y. Initial-Boundary Value Problems for Linear Dispersive Evolution Equations on the Half-Line. Preprint, 2001.
14. Ginibre, J.; Velo, G. Smoothing Properties and Retarded Estimates for Some Dispersive Evolution Equations. Comm. Math. Phys. 1992, 144, 163-188.
15. Hammack, J.L.; Segur, H. The Korteweg-de Vries Equation and Water Waves II. Comparison with Experiments. J. Fluid Mech. 1974, 65, 289-313.
16. Jerison, D.; Kenig, C. The Inhomogeneous Dirichlet Problem in Lipschitz Domains. J. Funct. Anal. 1995, 130(1), 161-219.
17. Kenig, C.; Ponce, G.; Vega, L. Oscillatory Integrals and Regularity of Dispersive Equations. Indiana Univ. Math. J. 1991, 40(1), 33-69.
18. Kenig, C.; Ponce, G.; Vega, L. The Cauchy Problem for the Korteweg-de Vries Equation in Sobolev Spaces of Negative Indices. Duke Math. J. 1993, 71, 1-21.
19. Kenig, C.; Ponce, G.; Vega, L. Well-Posedness and Scattering Results for the Generalized Korteweg-de Vries Equation, via the Contraction Principle. Communications on Pure and Applied Mathematics XLVI 1993, 527-560.
20. Kenig, C.; Ponce, G.; Vega, L. A Bilinear Estimate with Applications to the KdV Equation. J. Amer. Math. Soc. 1996, 9, 573-603.
21. 2. Contemp. Math. 2000, 263, 131-156.
22. Kenig, C.; Ponce, G.; Vega, L. On the Ill-Posedness of Some Canonical Dispersive Equations. Duke Math. J. 2001, 106, 617-633.
23. Stein, E.M. Singular Integrals and Differentiability Properties of Functions; Princeton University Press: Princeton, NJ, 1970.
24. Stein, E.M. Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. Annals of Mathematical Studies; No. 60, Princeton University Press: Princeton, NJ, 1970.
25. Stein, E.M. Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals; Princeton University Press: Princeton, NJ, 1993.
26. Stein, E.M.; Weiss, G. Introduction to Fourier Analysis on Euclidean Spaces; Princeton University Press: Princeton, NJ, 1971.