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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Properties of the solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension


Authors: Robert T. Glassey and John M. Chadam
Journal: Proc. Amer. Math. Soc. 43 (1974), 373-378
MSC: Primary 35QXX; Secondary 35B40
MathSciNet review: 0338586
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0338586-2
PII: S 0002-9939(1974)0338586-2
Keywords: Maxwell-Dirac equations, Cauchy problem, regularity, blowup, scattering, stationary solutions
Article copyright: © Copyright 1974 American Mathematical Society