Asymptotic behavior of an initial-boundary value problem for the Vlasov-Poisson-Fokker-Planck system

被引：48

作者：

Bonilla, LL ^{[1
]}

Carrillo, JA ^{[1
]}

Soler, J ^{[1
]}

机构：

[1] UNIV GRANADA,FAC CIENCIAS,DEPT MATEMAT APLICADA,E-18071 GRANADA,SPAIN

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1997年 / 57卷 / 05期

关键词：

boundary conditions for kinetic equations; Vlasov-Poisson-Fokker-Planck system; asymptotic behavior;

D O I：

10.1137/S0036139995291544

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The asymptotic behavior for the Vlasov-Poisson-Fokker-Planck system in bounded domains is analyzed in this paper. Boundary conditions defined by a scattering kernel are considered. It is proven that the distribution of particles tends for large time to a Maxwellian determined by the solution of the Poisson-Boltzmann equation with Dirichlet boundary condition. In the proof of the main result, the conservation law of mass and the balance of energy and entropy identities are rigorously derived. An important argument in the proof is to use a Lyapunov-type functional related to these physical quantities.

引用

页码：1343 / 1372

页数：30

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