Free access
Issue
ESAIM: M2AN
Volume 35, Number 2, March/April 2001
Page(s) 295 - 312
DOI http://dx.doi.org/10.1051/m2an:2001116
Published online 15 April 2002
  1. J.P. Aubin, Un théorème de compacité. C. R. Acad. Sci. Paris 256 (1963) 5042-5044. [MathSciNet]
  2. Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations 25 (2000) 737-754. [CrossRef] [MathSciNet]
  3. H. Brézis, F. Golse, R. Sentis, Analyse asymptotique de l'équation de Poisson couplée à la relation de Boltzmann. Quasi-neutralité des plasmas. C. R. Acad. Sci. Paris 321 (1995) 953-959.
  4. S. Cordier, P. Degond, P. Markowich, C. Schmeiser, Traveling wave analysis and jump relations for Euler-Poisson model in the quasineutral limit. Asymptot. Anal. 11 (1995) 209-224.
  5. S. Cordier, E. Grenier, Quasineutral limit of an Euler-Poisson system arising from plasma physics. Comm. Partial Differential Equations 25 (2000) 1099-1113. [CrossRef] [MathSciNet]
  6. P.C. Fife, Semilinear elliptic boundary value problems with small parameters. Arch. Rational Mech. Anal. 52 (1973) 205-232. [MathSciNet]
  7. H. Gajewski, On the uniqueness of solutions to the drift-diffusion model of semiconductor devices. Math. Models Methods Appl. Sci. 4 (1994) 121-133. [CrossRef] [MathSciNet]
  8. I. Gasser, The initial time layer problem and the quasi-neutral limit in a nonlinear drift diffusion model for semiconductors. Nonlinear Differential Equations Appl. (to appear).
  9. I. Gasser, D. Levermore, P. Markowich, C. Schmeiser, The initial time layer problem and the quasi-neutral limit in the drift-diffusion model (submitted).
  10. A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling. Math. Nachr. 185 (1997) 85-110. [MathSciNet]
  11. A. Jüngel, Y.J. Peng, A hierarchy of hydrodynamic models for plasmas. Zero-relaxation-time limits. Comm. Partial Differential Equations 24 (1999) 1007-1033. [CrossRef] [MathSciNet]
  12. A. Jüngel, Y.J. Peng, A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire 17 (2000) 83-118.
  13. A. Jüngel, Y.J. Peng, Zero-relaxation-time limits in hydrodynamic models for plasmas revisited. Z. Angew. Math. Phys. 51 (2000) 385-396. [CrossRef] [MathSciNet]
  14. A. Jüngel, Y.J. Peng, A hierarchy of hydrodynamic models for plasmas. Quasi-neutral limits in the drift-diffusion equations. Asymptot. Anal. (to appear).
  15. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod-Gauthier-Villard, Paris (1969).
  16. P.A. Markowich, A singular perturbation analysis of the fundamental semiconductor device equations. SIAM J. Appl. Math. 44 (1984) 896-928. [CrossRef] [MathSciNet]
  17. P.A. Markowich, C. Ringhofer, C. Schmeiser, An asymptotic analysis of one-dimensional models for semiconductor devices. IMA J. Appl. Math. 37 (1986) 1-24. [CrossRef] [MathSciNet]
  18. Y.J. Peng, Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for a nonlinear Euler-Poisson system. Nonlinear Anal. TMA 42 (2000) 1033-1054.
  19. P. Raviart, On singular perturbation problems for the nonlinear Poisson equation or: A mathematical approach to electrostatic sheaths and plasma erosion, Lect. Notes of the Summer school in Ile d'Oléron, France (1997) 452-539.
  20. L. Tartar, Compensated compactness and applications to partial differential equations. In: Nonlinear analysis and mechanics: Heriot-Watt Symp. Vol. 4 and Res. Notes Math. 3 (1979) 136-212.
  21. A. Visintin, Strong convergence results related to strict convexity. Comm. Partial Differential Equations 9 (1984) 439-466. [CrossRef] [MathSciNet]

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