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Global solutions to the isothermal Euler-Poisson plasma model. (English) Zbl 0817.76102
Summary: Global existence of a solution to the system of isothermal one- dimensional Euler equations for electrons and ions coupled by the Poisson equation is proved using Glimm scheme. The key point is the use of the almost conservation of charge for estimating the total variation of the electric field.

MSC:
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35Q35 PDEs in connection with fluid mechanics
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[1] Poupaud, F; Rascle, M; Vila, J.P, Global solutions to the isothermal Euler-Poisson system with arbitrary large data, J.p.d.e., (1993), (submitted) · Zbl 0845.35123
[2] Cordier, S; Degond, P; Markowich, P; Schmeiser, C, Travelling wave analysis and jump relations for the Euler-Poisson model in the quasineutral limit, Asymptotic analysis, (1994), (to appear) · Zbl 0874.76097
[3] Glimm, J, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. pure appl. math., 18, 698-715, (1965) · Zbl 0141.28902
[4] Nishida, T, Global solutions for an initial boundary value problem of a quasilinear hyperbolic system, Japan acad., 44, 642-646, (1968) · Zbl 0167.10301
[5] Cordier, S, Modélisation mathématique et simulation numérique du plasma magnétosphérique, Thèse de l’E.N.S. de cachan, (1994)
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