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Decay and scattering of solutions of a nonlinear Schrödinger equation. (English) Zbl 0395.35070


MSC:

35P25 Scattering theory for PDEs
47A10 Spectrum, resolvent
35Q99 Partial differential equations of mathematical physics and other areas of application
35G25 Initial value problems for nonlinear higher-order PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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References:

[1] J. Ginibre and G. Velo; J. Ginibre and G. Velo · Zbl 0396.35029
[2] Lin, J. E., Time Decay of Two Conservative Equations, (Ph.D. thesis (1976), Brown University)
[3] Morawetz, C. S., Notes on time decay and scattering for some hyperbolic problems (1975), SIAM · Zbl 0303.35002
[4] Morawetz, C. S.; Strauss, W. A., Decay and scattering of solutions of a nonlinear relativistic wave equation, Comm. Pure Appl. Math., 25, 1-31 (1972) · Zbl 0228.35055
[5] Pecher, H., Das Verhalten globaler Lösungen nichtlinearer Wellengleichungen für grosse Zeiten, (Doctoral Thesis (1974), Göttingen University) · Zbl 0265.35051
[6] Reed, M., Abstract Non-linear Wave Equations, (Lecture Notes in Mathematics No. 507 (1976), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York) · Zbl 0317.35002
[7] Segal, I. E., Nonlinear semigroups, Ann. of Math., 78, 339-364 (1963)
[8] Strauss, W. A., On weak solutions of semi-linear hyperbolic equations, An. Acad. Brasil Ci., 42, 645-651 (1970) · Zbl 0217.13104
[9] Strauss, W. A., Nonlinear scattering theory, (Scattering Theory in Mathematical Physics (1974), Reidel: Reidel Dordrecht), 53-78 · Zbl 0297.35062
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