Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for a nonlinear Euler-Poisson system

Nonlinear Analysis, Theory, Methods and Applications

Volumn 42, Issue 6, 2000, Pages 1033-1054

  Peng, Yue Jun ^a  

^a UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONS; IONS; PLASMAS; POISSON DISTRIBUTION;

EULER-POISSON SYSTEMS; GODUNOV METHOD; LAX-FRIEDRICH METHOD;

NONLINEAR EQUATIONS;

EID: 0343442476     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00168-6     Document Type: Article

References (23)

1. G.Q. Chen, The theory of compensated compactness and the system of isentropic gas dynamics, preprint, MCS-P154-0590, Univ. of Chicago, 1990.
2. Chen G.Q. Convergence of Lax-Friedrichs scheme for isentropic gas dynamics (III). Acta Math. Sci. 6:1986;75-120.
3. S. Cordier, Modélisation mathématique et simulation numérique du plasma magnétosphérique, Ph.D. Thesis, Ecole Normale Supérieure de Cachan, Paris, 1994.
4. Cordier S., Peng Y.J. Système Euler-Poisson non linéaire - Existence globale de solutions faibles entropiques. Mod. Math. Anal. Num. 32(1):1998;1-23.
5. X. Ding , G.Q. Chen, P. Luo, Convergence of Lax-Friedrichs scheme for isentropic gas dynamics (I) (II), Acta Math. Sci., 5, (1985) 483-500, 501-540.
6. Ding X., Chen G.Q., Luo P. Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for isentropic gas dynamics. Comm. Math. Phys. 121:1989;63-84.
7. DiPerna R.J. Convergence of approximate solutions of conservation laws. Arch. Rat. Mech. Anal. 82:1983;27-70.
8. N et quasineutralité, C.R. Acad. Sci. Paris, Série I, t. 320, 1995, 45-48.
9. Jüngel A. On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors. Math. Mod. Meth. Appl. Sci. 4(5):1994;677-703.
10. Jüngel A. A nonlinear drift-diffusion system with electric convection arising in electrophoretic and semiconductor modeling. Math. Nachr. 185:1997;85-110.
11. A. Jüngel, Y.J. Peng, A hierarchy of hydrodynamics models for plasmas, in preparation.
12. Lions P.L., Perthame B., Souganidis P.E. Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Comm. Pure Appl. Math. 49:1996;599-638.
13. Lions P.L., Perthame B., Tadmor E. Kinetic formulation for the isentropic gas dynamics and p-system. Comm. Math. Phys. 163:1994;415-431.
14. Liu T.P., Smoller J. The vacuum state in non-isentropic gas dynamics. Adv. Appl. Math. 1:1980;345-359.
15. Liu T.P., Smoller J. Le problème du vide pour les équations de la dynamique des gaz isentropiques. Res. Notes Math. 60:1981;319-326.
16. Marcati P., Natalini R. Weak solutions to a hydrodynamic model for semiconductors: the Cauchy problem. Proc. Roy. Soc. Edinburgh Sect. A. 125:1995;115-131.
17. Marcati P., Natalini R. Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch. Rat. Mech. Anal. 129:1995;129-145.
18. P.A. Markowich, C. Ringhofer, C. Schmeiser, Semiconductor Equations, Springer, Vienna / New-York, 1990.
19. Natalini R. The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation. J. Math. Anal. Appl. 198:1996;262-281.
20. Murat F. Compacité par compensation. Ann. Sc. Norm. Sup. Pisa. 5:1978;489-507.
21. Poupaud F., Rascle M., Vila J.P. Global solutions to the isothermal Euler-Poisson system with arbitrary large data. J. Differental Equations. 123:1995;93-121.
22. J. Smoller, Shock Waves and Reaction Diffusion Equations, Springer, Berlin, 1983.
23. L. Tartar, Compensated compactness and applications to partial differential equations, in: R.J. Knops (Ed.), Research Note in Mathematics, Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, vol. 4, Pitman Press, New York, 1979, pp. 136-212.