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On the existence of weak solutions for a nonlinear time dependent Dirac equation*

Published online by Cambridge University Press:  14 November 2011

João-Paulo Dias
Affiliation:
CMAF, 2 Av. Prof. Gama Pinto, 1699 Lisboa Codex, Portugal
Mário Figueira
Affiliation:
CMAF, 2 Av. Prof. Gama Pinto, 1699 Lisboa Codex, Portugal

Synopsis

In this paper we prove the existence of a weak solution of the Cauchy problem for the nonlinear Dirac equation in ℝ × ℝ

where X(r) is the characteristic function of a compact interval of ]0, + ∞[

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1989

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References

1Bjorken, J. D. and Drell, S. D.. Relativistic Quantum Mechanics (New York: McGraw-Hill, 1964).Google Scholar
2Cazenave, T. and Weissler, F.. The Cauchy problem for the nonlinear Schrödinger equation in H1. Manuscripta Math. 61 (1988), 477494.CrossRefGoogle Scholar
3Dias, J. P. and Figueira, M.. Sur l'existence d'une solution globale pour une équation de Dirac non linéaire avec masse nulle. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), 469472.Google Scholar
4Dias, J. P. and Figueira, M.. Remarque sur le problème de Cauchy pour une équation de Dirac non linéaire avec masse nulle. Portugal. Math. 45 (1988), 327335.Google Scholar
5Lions, J. L.. Quelques méthodes de résolution des problèmes aux limites non linéaires (Paris: Dunod, 1969).Google Scholar
6Reed, M.. Abstract Non-linear Wave Equations. Lecture Notes in Mathematics 507 (Berlin: Springer, 1976).CrossRefGoogle Scholar