Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations

 Access to full text

 Full (PDF)

1. [1] J.P. Aubin, Un théorème de compacité. C. R. Acad. Sci. Paris 256 (1963) 5042–5044. Zbl0195.13002
2. [2] Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm. Partial Differential Equations 25 (2000) 737–754. Zbl0970.35110
3. [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. Zbl0839.76096
4. [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. Zbl0849.35105
5. [5] S. Cordier, E. Grenier, Quasineutral limit of an Euler-Poisson system arising from plasma physics. Comm. Partial Differential Equations 25 (2000) 1099–1113. Zbl0978.82086
6. [6] P.C. Fife, Semilinear elliptic boundary value problems with small parameters. Arch. Rational Mech. Anal. 52 (1973) 205–232. Zbl0268.35007
7. [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. Zbl0801.35133
8. [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). Zbl0980.35158MR1841258
9. [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). Zbl1018.82024
10. [10] A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling. Math. Nachr. 185 (1997) 85–110. Zbl1157.35406
11. [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. Zbl0946.35074
12. [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. Zbl0956.35010
13. [13] A. Jüngel, Y.J. Peng, Zero-relaxation-time limits in hydrodynamic models for plasmas revisited. Z. Angew. Math. Phys. 51 (2000) 385–396. Zbl0963.35115
14. [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). Zbl1045.76058MR1865570
15. [15] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod-Gauthier-Villard, Paris (1969). Zbl0189.40603MR259693
16. [16] P.A. Markowich, A singular perturbation analysis of the fundamental semiconductor device equations. SIAM J. Appl. Math. 44 (1984) 896–928. Zbl0568.35007
17. [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. Zbl0639.34016
18. [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. Zbl0965.65113
19. [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. [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. Zbl0437.35004
21. [21] A. Visintin, Strong convergence results related to strict convexity. Comm. Partial Differential Equations 9 (1984) 439–466. Zbl0545.49019