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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 602753, 8 pages
Global Strong Solutions to Some Nonlinear Dirac Equations in Super-Critical Space
Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea
Received 10 April 2013; Accepted 21 May 2013
Academic Editor: Leszek Gasinski
Copyright © 2013 Hyungjin Huh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. Delgado, “Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac and other nonlinear Dirac equations in one space dimension,” Proceedings of the American Mathematical Society, vol. 69, no. 2, pp. 289–296, 1978.
- H. Huh, “Global strong solution to the Thirring model in critical space,” Journal of Mathematical Analysis and Applications, vol. 381, no. 2, pp. 513–520, 2011.
- E. Salusti and A. Tesei, “On a semi-group approach to quantum field equations,” Nuovo Cimento A, vol. 11, no. 2, pp. 122–138, 1971.
- S. Selberg and A. Tesfahun, “Low regularity well-posedness for some nonlinear Dirac equations in one space dimension,” Differential and Integral Equations, vol. 23, no. 3-4, pp. 265–278, 2010.
- N. Bournaveas, “Local well-posedness for a nonlinear Dirac equation in spaces of almost critical dimension,” Discrete and Continuous Dynamical Systems A, vol. 20, no. 3, pp. 605–616, 2008.
- T. Candy, “Global existence for an critical nonlinear Dirac equation in one dimension,” Advances in Differential Equations, vol. 16, no. 7-8, pp. 643–666, 2011.
- S. Machihara, “Dirac equation with certain quadratic nonlinearities in one space dimension,” Communications in Contemporary Mathematics, vol. 9, no. 3, pp. 421–435, 2007.
- S. Machihara, K. Nakanishi, and K. Tsugawa, “Well-posedness for nonlinear Dirac equations in one dimension,” Kyoto Journal of Mathematics, vol. 50, no. 2, pp. 403–451, 2010.
- S. Selberg, “Global well-posedness below the charge norm for the Dirac-Klein-Gordon system in one space dimension,” International Mathematics Research Notices, vol. 5, Article ID rnm058, 25 pages, 2007.
- R. H. Goodman, M. I. Weinstein, and P. J. Holmes, “Nonlinear propagation of light in one-dimensional periodic structures,” Journal of Nonlinear Science, vol. 11, no. 2, pp. 123–168, 2001.
- R. H. Goodman, R. E. Slusher, M. I. Weinstein, and M. Klaus, “Trapping light with grating defects,” in Mathematical Studies in Nonlinear Wave Propagation, vol. 379 of Contemporary Mathematics, pp. 83–92, 2005.
- M. A. Porter, M. Chugunova, and D. E. Pelinovsky, “Feshbach resonance management of BoseEinstein condensates in optical lattices,” Physical Review E, vol. 74, no. 3, Article ID 036610, 2006.
- S. Machihara and T. Omoso, “The explicit solutions to the nonlinear Dirac equation and Dirac-Klein-Gordon equation,” Ricerche di Matematica, vol. 56, no. 1, pp. 19–30, 2007.
- Y. Zhou, “Uniqueness of weak solutions of dimensional wave maps,” Mathematische Zeitschrift, vol. 232, no. 4, pp. 707–719, 1999.