Free access
Volume 40, Number 6, November-December 2006
Page(s) 1023 - 1052
Published online 15 February 2007
  1. M. Bostan, Solutions périodiques des équations d'évolution. C. R. Acad. Sci., Ser. I, Math. 332 (2001) 401–404.
  2. M. Bostan, Periodic solutions for evolution equations. Electron. J. Diff. Eqns., Monograph 3 (2002) 41.
  3. H. Brezis, Problèmes unilatéraux. J. Math. Pures Appl. 51 (1972) 1–64. [MathSciNet]
  4. R.C. Davidson and H. Qin, Physics of charged particle beams in high energy accelerators. Imperial College Press, World Scientific Singapore (2001).
  5. P. Degond and P.-A. Raviart, On the paraxial approximation of the stationary Vlasov-Maxwell system, Math. Models Meth. Appl. Sci. 3 (1993) 513–562.
  6. F. Filbet and E. Sonnendrücker, Modeling and numerical simulation of space charge dominated beams in the paraxial approximation. Research report INRIA, No. 5547 (2004).
  7. I.M. Kapchinsky and V.V. Vladimirsky, Proceedings of the 9th international conference on high energy accelerators, CERN Geneva (1959) 274.
  8. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Academic Press, New York, London (1980).
  9. G. Laval, S. Mas-Gallic and P.-A. Raviart, Paraxial approximation of ultra-relativistic intense beams. Numer. Math. 1 (1994) 33–60. [CrossRef]
  10. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non-linéaires. Dunod Gauthier-Villars (1969).
  11. Z. Meiyue, C. Taiyoung, L. Wenbin and J. Yong, Existence of positive periodic solution for the electron beam focusing system. Math. Meth. Appl. Sci. 28 (2005) 779–788. [CrossRef]
  12. A. Nouri, Paraxial approximation of the Vlasov-Maxwell system: laminar beams. Math. Models Meth. Appl. Sci. 4 (1994) 203–221. [CrossRef]
  13. P.-A. Raviart, Paraxial approximation of the stationary Vlasov-Maxwell equations, Nonlinear partial differential equations and their applications. Collège de France Seminar, vol. XIII Paris (1991–1993), Pitman Res. Notes Math. Ser., Longman Sci. Tech., Harlow 302 (1994) 158–171.
  14. M. Reiser, Theory and design of charged-particle beams. Wiley, New York (1994).

Recommended for you