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Nonlinear scattering theory at low energy. (English) Zbl 0466.47006

MSC:
47A40 Scattering theory of linear operators
35P25 Scattering theory for PDEs
47H20 Semigroups of nonlinear operators
81U05 \(2\)-body potential quantum scattering theory
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[1] {\scGuang-Chang Dong and Li Shujie}, On the initial value problem for a nonlinear Schrödinger equation, to appear.
[2] Ginibre, J; Velo, G, On a class of nonlinear Schrödinger equations, I, the Cauchy problem, J. functional analysis, 32, 1-32, (1979) · Zbl 0396.35028
[3] Ginibre, J; Velo, G, On a class of nonlinear Schrödinger equations, II, scattering theory, J. functional analysis, 32, 33-71, (1979) · Zbl 0396.35029
[4] Glassey, R.T, On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations, J. math. phys., 18, 1794-1797, (1977) · Zbl 0372.35009
[5] {\scR. T. Glassey}, Finite-time blow-up for solutions of nonlinear wave equations, to appear. · Zbl 0438.35045
[6] John, F, Blow-up of solutions of nonlinear wave equations in three dimensions, Manuscripta math., 28, 235-268, (1979) · Zbl 0406.35042
[7] {\scT. Kato}, Private communication, May 1980.
[8] {\scS. Klainerman}, Long time behavior of the solutions to nonlinear evolution equations, to appear. · Zbl 0502.35015
[9] {\scB. Marshall, W. Strauss, and S. Wainger}, Lp − Lq estimates for the Klein-Gordon equation, J. Math. Pures Appl., in press. · Zbl 0457.47040
[10] Reed, M, Abstract non-linear wave equations, () · Zbl 0317.35002
[11] Reed, M; Simon, B, (), Sect. XI. 13
[12] Segal, I.E, Non-linear semi-groups, Ann. of math., 78, 339-364, (1963) · Zbl 0204.16004
[13] Segal, I.E, Quantization and dispersion for non-linear relativistic equations, (), 79-108
[14] Segal, I.E, Dispersion for non-linear relativistic equations, II, Ann. sci. ecole norm. sup., 1, 459-497, (1968), (4) · Zbl 0179.42302
[15] Segal, I.E, Space-time decay for solutions of wave equations, Advances in math., 22, 304-311, (1976)
[16] Strauss, W.A, Nonlinear scattering theory, (), 53-78 · Zbl 0297.35062
[17] Strauss, W.A, Dispersion of low-energy waves for two conservative equations, Arch. rational mech. anal., 55, 86-92, (1974) · Zbl 0289.35048
[18] Strauss, W.A, Nonlinear invariant wave equations, (), 197-249
[19] Strauss, W.A, Everywhere defined wave operators, (), 85-102
[20] Strauss, W.A, Abstract 79T-B77, Amer. math. soc. notices, 26, A274, (1979)
[21] Strichartz, R.S, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke math. J., 44, 705-714, (1977) · Zbl 0372.35001
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