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On certain global solutions of the Cauchy problem for the (classical) coupled Klein-Gordon-Dirac equations in one and three space dimensions. (English) Zbl 0285.35042

35L15 Initial value problems for second-order hyperbolic equations
35P25 Scattering theory for PDEs
35B99 Qualitative properties of solutions to partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI
[1] Chadam, J. M., Global solutions of the Cauchy problem for the (classical) coupled Maxwell Dirac equations in one space dimension. J. Funct. Anal. 13, 173–184 (1973). · Zbl 0264.35058 · doi:10.1016/0022-1236(73)90043-8
[2] Chadam, J. M., On the Cauchy problem for the coupled Maxwell-Dirac equations. J. Math. Phys. 5, 597–604 (1972). · Zbl 0228.35075 · doi:10.1063/1.1666021
[3] Chadam, J. M., Asymptotics for u=m2u+G(x, t, u, ux, ut), I and II. Ann. Scuola Norm. Sup. (Pisa) 26, 33–65 and 67–95 (1972). · Zbl 0241.35014
[4] Chadam, J. M., & R. T. Glassey, Properties of the solutions of the (classical) coupled Maxwell-Dirac equations in one space dimension. To appear in Proc. Amer. Math. Soc. · Zbl 0258.35004
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[8] Segal, I., Nonlinear semi-groups. Ann. Math. 78, 339–364 (1963). · Zbl 0204.16004 · doi:10.2307/1970347
[9] Segal, I., Quantization and Dispersion for Nonlinear Relativistic Equations in Mathematical Theory of Elementary Particles. M.I.T. Press, Cambridge, Mass., 1966, 79–108.
[10] Strauss, W., Decay and asymptotics for u=F(u). J. Funct. Anal. 2, 409–457 (1968). · Zbl 0182.13602 · doi:10.1016/0022-1236(68)90004-9
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[12] Howland, J., Stationary Scattering Theory for Time-dependent Hamiltonians, preprint, Aug. 1973.
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