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, p. 83-118
@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},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {1},
     year = {2000},
     pages = {83-118},
     zbl = {0956.35010},
     mrnumber = {1743432},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/AIHPC_2000__17_1_83_0/

[1] S. Antontsev, A. Domansky and J.I. Díaz, Continuous dependence and stabilization of solutions of the degenerate system in two-phase filtration, Dinamika Sploshnoi Sredy 107 (1993) 11-25. | MR 1304988 | Zbl 0831.76078

[2] H. Beirao Da Veiga, On the W2,p-regularity for solutions of mixed problems, J. Math. Pures Appl. 53 (1974) 279-290. | Zbl 0264.35017

[3] H. Brézis, 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 1260437 | Zbl 0813.49016

[4] S. Cordier, Global solutions to the isothermal Euler-Poisson plasma model, Appl. Math. Lett. 8 (1994) 19-24. | MR 1355145 | Zbl 0817.76102

[5] S. Cordier and Y.-J. Peng, Système Euler-Poisson non linéaire-existence globale de solutions faibles entropiques, Mod. Math. Anal. Num. 32 (1998) 1-23. | Numdam | MR 1619591 | Zbl 0935.35119

[6] J.I. Díaz, G. Galiano and A. Jüngel, On a quasilinear degenerate system arising in semiconductor theory, Part I: Existence and uniqueness of solutions, To appear in Nonlin. Anal. TMA (2000).

[7] J.I. Díaz, G. Galiano and A. Jüngel, 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 1464818 | Zbl 0883.35007

[8] G. Gagneux and M. Madaune-Tort, Sur la question de l'unicité pour les inéquations des milieux poreux, C. R. Acad. Sci. Paris 314 (1992) 605-608. | MR 1158745 | Zbl 0746.76082

[9] C. Gardner, Numerical simulation of a steady-state electron shock wave in a submicron semiconductor device, IEEE Trans. El. Dev. 38 (1991) 392-398.

[10] T. Goudon, A. Jüngel and Y-J. Peng, Zero-electron-mass limits in hydrodynamic models for plasmas, Appl. Math. Lett. 12 (1999) 75-79. | MR 1750602 | Zbl 0959.76096

[11] K. Gröger and J. Rehberg, Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities, Math. Z. 213 (1993) 523-530. | MR 1231876 | Zbl 0790.35049

[12] X. Jiang, A streamline-upwinding/Petrov-Galerkin method for the hydrodynamic semiconductor device model, Math. Models Meth. Appl. Sci. 5 (1995) 659-681. | MR 1347152 | Zbl 0833.76036

[13] A. Jüngel, 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 1300812 | Zbl 0820.35128

[14] A. Jüngel, Numerical approximation of a drift-diffusion model for semiconductors with nonlinear diffusion, Z. Angew. Math. Mech. 75 (1995) 783-799. | MR 1358825 | Zbl 0866.35056

[15] A. Jüngel, Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Meth. Appl. Sci. 5 (1995) 497- 518. | MR 1335830 | Zbl 0841.35114

[16] A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling, Math. Nachr. 185 (1997) 85-110. | MR 1452478 | Zbl 01019611

[17] A. Jüngel and Y.-J. Peng, A hierarchy of hydrodynamic plasma models. Zero-relaxation-time limits, Comm. P. D. E. 24 (1999) 1007-1033. | MR 1680885 | Zbl 0946.35074

[18] O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Ural'Ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968.

[19] P.A. Markowich, The Stationary Semiconductor Device Equations, Springer, Wien, 1986. | MR 821965

[20] P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 115-131. | MR 1318626 | Zbl 0831.35157

[21] P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Rat. Mech. Anal. 129 (1995) 129-145. | MR 1328473 | Zbl 0829.35128

[22] R. Natalini, The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation, J. Math. Anal. Appl. 198 (1996) 262-281. | MR 1373540 | Zbl 0889.35109

[23] Y-J. Peng, Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for a nonlinear Euler-Poisson system, Nonlin. Anal. (1999) (to appear). | MR 1780453 | Zbl 0965.65113

[24] F. Poupaud, M. Rascle and J. Vila, Global solutions to the isothermal Euler-Poisson system with arbitrarily large data, J. Differential Equations 123 (1995) 93-121. | MR 1359913 | Zbl 0845.35123

[25] P. Raviart, 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] J. Simon, Compact sets in the space Lp(0, T; B), Ann. Math. Pura Appl. 146 (1987) 65-96. | MR 916688 | Zbl 0629.46031

[27] G. Stampacchia, Equations Elliptiques du Second Ordre à Coefficients Disconti- nus, Les Presses de l'Université de Montréal, Canada, 1966. | MR 251373 | Zbl 0151.15501

[28] G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. | MR 1094820 | Zbl 0655.35002

[29] A. Visintin, Strong convergence results related to strict convexity, Comm. Partial Differential Equations 9 (1984) 439-466. | MR 741216 | Zbl 0545.49019

[30] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II, Springer, New York, 1990.