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High-field limit for the Vlasov-Poisson-Fokker-Planck system. (English) Zbl 1038.82068
Summary: This paper is concerned with the analysis of the stability of the Vlasov-Poisson-Fokker-Planck system with respect to the physical constants. If the scaled thermal mean free path converges to zero and the scaled thermal velocity remains constant, then a hyperbolic limit or equivalently a high-field limit equation is obtained for the mass density. The passage to the limit as well as the existence and uniqueness of solutions of the limit equation in \(L^1\), global or local in time, are analyzed according to the electrostatic or gravitational character of the field and to the space dimension. In the one-dimensional case a new concept of global solution is introduced. For the gravitational field this concept is shown to be equivalent to the concept of entropy solutions of hyperbolic systems of conservation laws.

MSC:
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
82D10 Statistical mechanics of plasmas
35B40 Asymptotic behavior of solutions to PDEs
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