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 (2000)
- Volume: 17, Issue: 1, page 83-118
- ISSN: 0294-1449
Access Full Article
topHow to cite
topJüngel, Ansgar, and 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 17.1 (2000): 83-118. <http://eudml.org/doc/78488>.
@article{Jüngel2000,
author = {Jüngel, Ansgar, Peng, Yue-Jun},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Euler-Poisson system; zero-relaxation-time limit; quasilinear parabolic equations; asymptotic limit; elliptic parabolic systems},
language = {eng},
number = {1},
pages = {83-118},
publisher = {Gauthier-Villars},
title = {A hierarchy of hydrodynamic models for plasmas. Zero-electron-mass limits in the drift-diffusion equations},
url = {http://eudml.org/doc/78488},
volume = {17},
year = {2000},
}
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
PB - Gauthier-Villars
VL - 17
IS - 1
SP - 83
EP - 118
LA - eng
KW - Euler-Poisson system; zero-relaxation-time limit; quasilinear parabolic equations; asymptotic limit; elliptic parabolic systems
UR - http://eudml.org/doc/78488
ER -
References
top- [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 Sredy107 (1993) 11-25. Zbl0831.76078MR1304988
- [2] H. Beirao Da Veiga, On the W2,p-regularity for solutions of mixed problems, J. Math. Pures Appl.53 (1974) 279-290. Zbl0264.35017
- [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. Zbl0813.49016MR1260437
- [4] S. Cordier, Global solutions to the isothermal Euler-Poisson plasma model, Appl. Math. Lett.8 (1994) 19-24. Zbl0817.76102MR1355145
- [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. Zbl0935.35119MR1619591
- [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). Zbl0994.35072
- [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. Paris325 (1997) 267-272. Zbl0883.35007MR1464818
- [8] G. Gagneux and M. Madaune-Tort, Sur la question de l'unicité pour les inéquations des milieux poreux, C. R. Acad. Sci. Paris314 (1992) 605-608. Zbl0746.76082MR1158745
- [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. Zbl0959.76096MR1750602
- [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. Zbl0790.35049MR1231876
- [12] X. Jiang, A streamline-upwinding/Petrov-Galerkin method for the hydrodynamic semiconductor device model, Math. Models Meth. Appl. Sci.5 (1995) 659-681. Zbl0833.76036MR1347152
- [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. Zbl0820.35128MR1300812
- [14] A. Jüngel, Numerical approximation of a drift-diffusion model for semiconductors with nonlinear diffusion, Z. Angew. Math. Mech.75 (1995) 783-799. Zbl0866.35056MR1358825
- [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. Zbl0841.35114MR1335830
- [16] A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling, Math. Nachr.185 (1997) 85-110. Zbl1157.35406MR1452478
- [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. Zbl0946.35074MR1680885
- [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. MR821965
- [20] P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem, Proc. Roy. Soc. Edinburgh Sect. A125 (1995) 115-131. Zbl0831.35157MR1318626
- [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. Zbl0829.35128MR1328473
- [22] R. Natalini, The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation, J. Math. Anal. Appl.198 (1996) 262-281. Zbl0889.35109MR1373540
- [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). Zbl0965.65113MR1780453
- [24] F. Poupaud, M. Rascle and J. Vila, Global solutions to the isothermal Euler-Poisson system with arbitrarily large data, J. Differential Equations123 (1995) 93-121. Zbl0845.35123MR1359913
- [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. Zbl0629.46031MR916688
- [27] G. Stampacchia, Equations Elliptiques du Second Ordre à Coefficients Disconti- nus, Les Presses de l'Université de Montréal, Canada, 1966. Zbl0151.15501MR251373
- [28] G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. Zbl0655.35002MR1094820
- [29] A. Visintin, Strong convergence results related to strict convexity, Comm. Partial Differential Equations9 (1984) 439-466. Zbl0545.49019MR741216
- [30] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II, Springer, New York, 1990. Zbl0684.47029
Citations in EuDML Documents
top- Yue-Jun Peng, Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations
- Didier Bresch, Benoît Desjardins, Bernard Ducomet, Quasi-neutral limit for a viscous capillary model of plasma
- Yue-Jun Peng, Boundary layer analysis and quasi-neutral limits in the drift-diffusion equations
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.