ASYMPTOTIC-BEHAVIOR OF AN INITIAL-BOUNDARY VALUE-PROBLEM FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM

The asymptotic behavior for the Vlasov-Poisson-Fokker-Planck system in bounded domains is analyzed in this paper. Boundary conditions define d by a scattering kernel are considered. It is proven that the distrib ution 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 m ass and the balance of energy and entropy identities are rigorously de rived. An important argument in the proof is to use a Lyapunov-type fu nctional related to these physical quantities.