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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 632903, 9 pages
http://dx.doi.org/10.1155/2013/632903
Research Article

Large Time Behavior of the Vlasov-Poisson-Boltzmann System

1Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150080, China
3Department of Foundation, Harbin Finance University, Harbin 150030, China

Received 18 May 2013; Accepted 1 July 2013

Academic Editor: Daniel C. Biles

Copyright © 2013 Li Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The motion of dilute charged particles can be modeled by 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 VPB system tends to global Maxwellian state in a rate , by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005). The improvement of the present paper is the removal of condition on parameter as in the work of Li (2008).