@article{AIHPC_2000__17_1_83_0, author = {J\"ungel, Ansgar and Peng, Yue-Jun}, title = {A hierarchy of hydrodynamic models for plasmas. {Zero-electron-mass} limits in the drift-diffusion equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {83--118}, publisher = {Gauthier-Villars}, volume = {17}, number = {1}, year = {2000}, mrnumber = {1743432}, zbl = {0956.35010}, language = {en}, url = {http://archive.numdam.org/item/AIHPC_2000__17_1_83_0/} }
TY - JOUR AU - Jüngel, Ansgar AU - Peng, Yue-Jun TI - A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2000 SP - 83 EP - 118 VL - 17 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_2000__17_1_83_0/ LA - en ID - AIHPC_2000__17_1_83_0 ER -
%0 Journal Article %A Jüngel, Ansgar %A Peng, Yue-Jun %T A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations %J Annales de l'I.H.P. Analyse non linéaire %D 2000 %P 83-118 %V 17 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPC_2000__17_1_83_0/ %G en %F AIHPC_2000__17_1_83_0
Jüngel, Ansgar; Peng, Yue-Jun. A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations. Annales de l'I.H.P. Analyse non linéaire, Volume 17 (2000) no. 1, pp. 83-118. http://archive.numdam.org/item/AIHPC_2000__17_1_83_0/
[1] Continuous dependence and stabilization of solutions of the degenerate system in two-phase filtration, Dinamika Sploshnoi Sredy 107 (1993) 11-25. | MR | Zbl
, and ,[2] On the W2,p-regularity for solutions of mixed problems, J. Math. Pures Appl. 53 (1974) 279-290. | Zbl
,[3] Convergence in D' and in L1 under strict convexity, in: J.-L. Lions (Ed.), Boundary Value Problems for Partial Differential Equations and Applications, Res. Notes Appl. Math. 29, Masson, 1993, pp. 43-52. | MR | Zbl
,[4] Global solutions to the isothermal Euler-Poisson plasma model, Appl. Math. Lett. 8 (1994) 19-24. | MR | Zbl
,[5] Système Euler-Poisson non linéaire-existence globale de solutions faibles entropiques, Mod. Math. Anal. Num. 32 (1998) 1-23. | Numdam | MR | Zbl
and ,[6] On a quasilinear degenerate system arising in semiconductor theory, Part I: Existence and uniqueness of solutions, To appear in Nonlin. Anal. TMA (2000).
, and ,[7] Space localization and uniqueness of vacuum solutions to a degenerate parabolic problem in semiconductor theory, C. R. Acad. Sci. Paris 325 (1997) 267-272. | MR | Zbl
, and ,[8] Sur la question de l'unicité pour les inéquations des milieux poreux, C. R. Acad. Sci. Paris 314 (1992) 605-608. | MR | Zbl
and ,[9] Numerical simulation of a steady-state electron shock wave in a submicron semiconductor device, IEEE Trans. El. Dev. 38 (1991) 392-398.
,[10] Zero-electron-mass limits in hydrodynamic models for plasmas, Appl. Math. Lett. 12 (1999) 75-79. | MR | Zbl
, and ,[11] Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities, Math. Z. 213 (1993) 523-530. | MR | Zbl
and ,[12] A streamline-upwinding/Petrov-Galerkin method for the hydrodynamic semiconductor device model, Math. Models Meth. Appl. Sci. 5 (1995) 659-681. | MR | Zbl
,[13] On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Meth. Appl. Sci. 4 (1994) 677-703. | MR | Zbl
,[14] Numerical approximation of a drift-diffusion model for semiconductors with nonlinear diffusion, Z. Angew. Math. Mech. 75 (1995) 783-799. | MR | Zbl
,[15] Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Meth. Appl. Sci. 5 (1995) 497- 518. | MR | Zbl
,[16] A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling, Math. Nachr. 185 (1997) 85-110. | MR | Zbl
,[17] A hierarchy of hydrodynamic plasma models. Zero-relaxation-time limits, Comm. P. D. E. 24 (1999) 1007-1033. | MR | Zbl
and ,[18] Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968.
, and ,[19] The Stationary Semiconductor Device Equations, Springer, Wien, 1986. | MR
,[20] Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 115-131. | MR | Zbl
and ,[21] Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Rat. Mech. Anal. 129 (1995) 129-145. | MR | Zbl
and ,[22] The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation, J. Math. Anal. Appl. 198 (1996) 262-281. | MR | Zbl
,[23] Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for a nonlinear Euler-Poisson system, Nonlin. Anal. (1999) (to appear). | MR | Zbl
,[24] Global solutions to the isothermal Euler-Poisson system with arbitrarily large data, J. Differential Equations 123 (1995) 93-121. | MR | Zbl
, and ,[25] On singular perturbation problems for the nonlinear Poisson equation or: A mathematical approach to electrostatic sheaths and plasma erosion, Lecture Notes of the Summer School in Ile d'Oléron, France, 1997, pp. 452-539.
,[26] Compact sets in the space Lp(0, T; B), Ann. Math. Pura Appl. 146 (1987) 65-96. | MR | Zbl
,[27] Equations Elliptiques du Second Ordre à Coefficients Disconti- nus, Les Presses de l'Université de Montréal, Canada, 1966. | MR | Zbl
,[28] Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. | MR | Zbl
,[29] Strong convergence results related to strict convexity, Comm. Partial Differential Equations 9 (1984) 439-466. | MR | Zbl
,[30] Nonlinear Functional Analysis and its Applications, Vol. II, Springer, New York, 1990.
,