Boundary layers and quasi-neutral limit in steady state Euler-Poisson equations for potential flows

Nonlinearity

Volumn 17, Issue 3, 2004, Pages 835-849

  Peng, Yue Jun ^a   Wang, Ya Guang ^b  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442681878     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/17/3/006     Document Type: Article

References (18)

1. Brézis H, Golse F and Sentis R 1995 Analyse asymptotique de l'équation de Poisson couplée à la relation de Boltzmann. Quasi-neutralité des plasmas C. R. Acad. Sci. Paris 321 953-9
2. Chen F 1984 Introduction to Plasma Physics and Controlled Fusion vol 1 (New York: Plenum)
3. Cordier S and Grenier E 2000 Quasineutral limit of an Euler-Poisson system arising from plasma physics Commun. Part. Diff. Eqns 25 1099-113
4. Degond P and Markowich P 1990 On a one-dimensional steady-state hydrodynamic model for semiconductors Appl. Math. Lett. 3 25-9
5. Degond P and Markowich P 1993 A steady state potential flow model for semiconductors Ann. Mat. Pura Appl. IV 87-98
6. Fife P C 1973 Semilinear elliptic boundary value problems with small parameters Arch. Ration. Mech. Anal. 52 205-32
7. Gamba I M 1992 Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors Commun. Part. Diff. Eqns 17 553-77
8. Gamba I M and Morawetz C S 1996 A viscous approximation for a 2-D steady semiconductor or transonic gas dynamic flow: existence theorem for potential flow Commun. Pure Appl. Math. XLIX 999-1049
9. Gilbarg D and Trudinger N S 1984 Elliptic Partial Differential Equations of Second Order 2nd edn (New York: Springer)
10. Grenier E and Guès O 1998 Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems J. Diff. Eqns 143 110-46
11. Guckenheimer J and Holmes P 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (New York: Springer)
12. Kopell N and Howard L N 1974 Bifurcations under nongeneric conditions Adv. Math. 13 274-83
13. Kopell N and Howard L N 1975 Bifurcations and trajectories joining critical points Adv. Math. 18 306-58
14. Markowich P 1986 The Stationary Semiconductor Device Equations (New York: Springer)
15. Peng Y J 2002 Asymptotic limits of one-dimensional hydrodynamic models for plasmas and semiconductors Chin. Ann. Math. B 23 25-36
16. Peng Y J 2003 Some asymptotic analysis in steady-state Euler-Poisson equations for potential flow Asymptotic Anal. 36 75-92
17. Peng Y J and Wang Y G Convergence of compressible Euler-Poisson equations to incompressible type Euler equations SIAM J. Math. Analysis submitted
18. Slemrod M and Sternberg N 2001 Quasi-neutral limit for the Euler-Poisson system J. Nonlinear Sci. 11 193-209