A hierarchy of hydrodynamic models for plasmas. Quasi-neutral limits in the drift-diffusion equations

Asymptotic Analysis

Volumn 28, Issue 1, 2001, Pages 49-73

  Jüngel, Ansgar ^a,b   Peng, Yue Jun ^c  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^c UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

Asymptotic analysis; Boundary layers; Drift diffusion equations; Entropy method; Plasmas; Singular perturbation

Indexed keywords

EID: 0035473786     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. H. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341.
2. A. Arnold, P. Markowich, G. Toscani and A. Unterreiter, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. Partial Differential Equations 26 (2001), 43-100.
3. J.P. Aubin, Un théorème de compacité. C. R. Acad. Sci. Paris 256 (1963), 5042-5044.
4. F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. Var. 1 (1993), 123-148.
5. Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations 25 (2000), 737-754.
6. H. Brezis, F. Golse and 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.
7. J. Carrillo, A. Jüngel, P. Markowich, G. Toscani and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatsh. Math., 2000, submitted.
8. 1-decay of solutions of the porous media equation to self-similarity, Indiana Univ. Math. J. 49 (2000), 113-142.
9. F. Chen, Introduction to Plasma Physics and Controlled Fusion, Vol. 1, Plenum Press, New York, 1984.
10. S. Cordier, P. Degond, P. Markowich and C. Schmeiser, Quasineutral limit of traveling waves for the Euler-Poisson model, in: Mathematical and Numerical Aspects of Wave Propagation, G. Cohen, ed., Proceedings of the 3rd International Conference, Mandelieu-La Napoule, France, Philadelphia, 1995, pp. 724-733.
11. S. Cordier, P. Degond, P. Markowich and C. Schmeiser, Traveling wave analysis and jump relations for Euler-Poisson model in the quasineutral limit, Asymptotic Anal. 11 (1995), 209-224.
12. S. Cordier and E. Grenier, Quasineutral limit of an Euler-Poisson system arising from plasma physics, Comm. Partial Differential Equations 25 (2000), 1099-1113.
13. G. Gagneux and M. Madaune-Tort, Analyse Mathématique de Modèles Non Linéaires de l'Ingénierie Pétrolière, Springer, Paris, 1996.
14. H. Gajewski, On existence, uniqueness and asymptotic behavior of solutions of the basic equations for carrier transport in semiconductors, Z. Angew. Math. Mech. 65 (1985), 101-108.
15. I. Gasser, The initial time layer problem and the quasineutral limit in a nonlinear drift diffusion model for semiconductors, Nonlinear Differential Equations Appl. 8 (2001), 237-249.
16. I. Gasser, D. Levermore, P. Markowich and C. Schmeiser, The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model, Preprint No. 859, Erwin-Schrödinger-Institute, Wien, 2000.
17. T. Goudon, A. Jüngel and Y. J. Peng, Zero-electron-mass limits in hydrodynamic models for plasmas, Appl. Math. Lett. 12 (1999), 75-79.
18. A. Jüngel, On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci. 4 (1994), 677-703.
19. A. Jüngel, Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci. 5 (1995), 497-518.
20. A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling, Math. Nachr. 185 (1997), 85-110.
21. A. Jüngel and Y.J. Peng, A hierarchy of hydrodynamic models for plasmas. Zero-relaxation-time limits, Comm. Partial Differential Equations 24 (1999), 1007-1033.
22. A. Jüngel and 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.
23. A. Jüngel and Y.J. Peng, Zero-relaxation-time limits in hydrodynamic models for plasmas revisited, Z. Angew. Math. Phys. 51 (2000), 385-396.
24. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod-Gauthier-Villard, Paris, 1969.
25. P.A. Markowich, C. Ringhofer and C. Schmeiser, An asymptotic analysis of one-dimensional models for semiconductor devices, IMA J. Appl. Math. 37 (1986), 1-24.
26. F. Otto, The geometry of dissipative evolution equations: the porous medium equation, Preprint No. 8, Max-Planck-Institut für Mathematik, Leipzig, Germany, 1999.
27. L. Tartar, Compensated compactness and applications to partial differential equations, in: Nonlinear Analysis and Mechanics: Heriot-Watt Symp., Vol. 4, Res. Notes Math., Vol. 39, 1979, pp. 136-212.
28. G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987.
29. A. Visintin, Strong convergence results related to strict convexity, Comm. Partial Differential Equations 9 (1984), 439-466.