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Large time behavior of the Vlasov-Poisson-Boltzmann system. (English) Zbl 1432.35200

Summary: The motion of dilute charged particles can be modeled by the Vlasov-Poisson-Boltzmann system. We study the large time stability of the VPB system. To be precise, we prove that when time goes to infinity, the solution of the VPB system tends to global Maxwellian state in a rate \(O \left(t^{- \infty}\right)\), by using a method developed for the Boltzmann equation without force in the work of L. Desvillettes and C. Villani [Invent. Math. 159, No. 2, 245–316 (2005; Zbl 1162.82316)]. The improvement of the present paper is the removal of a condition on the parameter \(\lambda\) as in the work of L. Li [J. Differ. Equations 244, No. 6, 1467–1501 (2008; Zbl 1151.35077)].

MSC:

35Q83 Vlasov equations
82D10 Statistical mechanics of plasmas
35B40 Asymptotic behavior of solutions to PDEs
35Q20 Boltzmann equations
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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References:

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