On nonlinear Schrödinger equations in exterior domains
Tài liệu tham khảo
Ben Artzi, 1992, Decay and regularity for the Schrödinger equation, J. Anal. Math., 58, 25, 10.1007/BF02790356
Bergh, 1976
Bourgain, 1999, Global Solutions of Nonlinear Schrödinger Equations, 10.1090/coll/046
Bourgain, 2000, Problems in Hamiltonian PDE's. GAFA 2000 (Tel Aviv, 1999), Geom. Funct. Anal. (Special Volume, Part I), 32
Brézis, 1980, Nonlinear Schrödinger evolution equations, Nonlinear Anal., 4, 677, 10.1016/0362-546X(80)90068-1
Burq, 1997, Contrôle de l’équation des ondes dans des ouverts peu réguliers, Asymptotic Anal., 14, 157, 10.3233/ASY-1997-14203
Burq, 1998, Décroissance de l’énergie locale de l’équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel, Acta Math., 180, 1, 10.1007/BF02392877
Burq, 2002, Semi-classical estimates for the resolvent in nontrapping geometries, Internat. Math. Res. Notices, 221, 10.1155/S1073792802103059
N. Burq, P. Gérard, N. Tzvetkov, Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds, Amer. J. Math., in press
Burq, 2003, The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold, Proceedings of the Öresund Symposium on Partial Differential Equations, Lund, May 23–25, 2002, J. Nonlinear Math. Phys., 10, 12, 10.2991/jnmp.2003.10.s1.2
Burq, 2003, Two singular dynamics of the nonlinear Schrödinger equation on a plane domain, Geom. Funct. Anal., 13, 1, 10.1007/s000390300000
Burq, 2002, An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains
Cazenave, 1993, An introduction to nonlinear Schrödinger equations, second ed., Textos de Métodos Matemáticos, 26
Constantin, 1988, Local smoothing properties of dispersive equations, J. Amer. Math. Soc., 1, 413, 10.1090/S0894-0347-1988-0928265-0
Constantin, 1989, Local smoothing properties of Schrödinger equations, Indiana Univ. Math. J., 38, 791, 10.1512/iumj.1989.38.38037
Christ, 2001, Maximal functions associated to filtrations, J. Funct. Anal., 179, 409, 10.1006/jfan.2000.3687
Doi, 1996, Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math. J., 82, 679, 10.1215/S0012-7094-96-08228-9
Kato, 1987, On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor., 46, 113
Kavian, 1987, A remark on the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, Trans. Amer. Math. Soc., 299, 193
S. Keraani, Étude de quelques régimes asymptotiques de l’équation de Schrödinger, PhD Thesis, Université de Paris-Sud, December 2000
Lax, 1989, Scattering Theory, vol. 26
Lions, 1969
Melrose, 1978, Singularities of boundary value problems I, Comm. Pure Appl. Math., 31, 593, 10.1002/cpa.3160310504
Melrose, 1982, Singularities of boundary value problems II, Comm. Pure Appl. Math., 35, 129, 10.1002/cpa.3160350202
Ogawa, 1991, Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger equations, J. Math. Anal. Appl., 155, 531, 10.1016/0022-247X(91)90017-T
Segal, 1963, Nonlinear semi-groups, Ann. Math., 78, 339, 10.2307/1970347
Sulem, 1999, The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, vol. 139
Sjölin, 1987, Regularity of solutions to Schrödinger equations, Duke Math. J., 55, 699, 10.1215/S0012-7094-87-05535-9
Smith, 1995, On the critical semilinear wave equation outside convex obstacles, J. Amer. Math. Soc., 8, 879, 10.1090/S0894-0347-1995-1308407-1
Staffilani, 2002, Strichartz estimates for a Schrödinger operator with nonsmooth coefficients, Comm. Partial Differential Equations, 27, 1337, 10.1081/PDE-120005841
Taylor, 1996, Partial Differential Equations
Tsutsumi, 1989, On smooth solutions to the initial-boundary value problem for the nonlinear Schrödinger equation in two space dimensions, Nonlinear Anal., 13, 1051, 10.1016/0362-546X(89)90094-1
Tsutsumi, 1991, On global solutions to the initial-boundary value problem for the nonlinear Schrödinger equation in exterior domains, Comm. Partial Differential Equations, 16, 885, 10.1080/03605309108820784
Tsutsumi, 1984, Global solutions of the nonlinear Schrödinger equation in exterior domains, Comm. Partial Differential Equations, 8, 1337, 10.1080/03605308308820306
Vainberg, 1988
Vasy, 2000, Semiclassical estimates in asymptotically euclidean scattering, Comm. Math. Phys., 212, 205, 10.1007/s002200000207
Vega, 1988, Schrödinger equations: pointwise convergence to the initial data, Proc. Amer. Math. Soc., 102, 874
Vladimirov, 1984, On the solvability of mixed problem for a nonlinear equation of Schrödinger type, Soviet Math. Dokl., 29, 281