Properties of the solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
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- by Robert T. Glassey and John M. Chadam PDF
- Proc. Amer. Math. Soc. 43 (1974), 373-378 Request permission
Abstract:
Solutions of the Maxwell-Dirac equations coupled through the standard electromagnetic interaction are shown to blow up at each spatial point for large times. This is used to show that these solutions do not tend asymptotically to free solutions. In addition it is used to prove that these equations do not admit a nontrivial stationary solution.References
- John M. Chadam, Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension, J. Functional Analysis 13 (1973), 173–184. MR 0368640, DOI 10.1016/0022-1236(73)90043-8
- Leonard Gross, The Cauchy problem for the coupled Maxwell and Dirac equations, Comm. Pure Appl. Math. 19 (1966), 1–15. MR 190520, DOI 10.1016/S0079-8169(08)61684-0
- Melvyn S. Berger, On the existence and structure of stationary states for a nonlinear Klein-Gordon equation, J. Functional Analysis 9 (1972), 249–261. MR 0299966, DOI 10.1016/0022-1236(72)90001-8
- Irving Segal, Non-linear semi-groups, Ann. of Math. (2) 78 (1963), 339–364. MR 152908, DOI 10.2307/1970347
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 373-378
- MSC: Primary 35QXX; Secondary 35B40
- DOI: https://doi.org/10.1090/S0002-9939-1974-0338586-2
- MathSciNet review: 0338586