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Cauchy problem for the Vlasov-Poisson-Boltzmann system. (English) Zbl 1104.76086
Summary: The dynamics of dilute electrons can be modelled by fundamental Vlasov-Poisson-Boltzmann system which describes mutual interactions of electrons through collisions in a self-consistent electric field. In this paper, it is shown that any smooth perturbation of a given global Maxwellian leads to a unique global-in-time classical solution when either the mean free path is small or the background charge density is large. Moreover, the solution converges to global Maxwellian when time tends to infinity. The analysis combines the techniques used in the study of conservation laws with the decomposition of Boltzmann equation introduced by T.-P. Liu et al. [Phys. D 188, No. 3–4, 178–192 (2004; Zbl 1098.82618)] and T.-P. Liu and S.-H. Yu [Commun. Math. Phys. 246, No. 1, 133–179 (2004; Zbl 1092.82034)] by obtaining new entropy estimates for this physical model.
MSC:
76X05Ionized gas flow in electromagnetic fields; plasmic flow
76P05Rarefied gas flows, Boltzmann equation
45K05Integro-partial differential equations
References:
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