On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with coulombic and newtonian potentials

Abstract

We prove that the solution of the Vlasov-Fokker-Planck equation converges to the unique stationary solution with same mass as time tends to infinity. The same result holds in the repulsive coulombic case for the Vlasov-Poisson-Fokker-Planck system; the newtonian attractive case is also studied. We establish positive and negative answers to the question of existence of a stationary solution for the last problem by examining the Poisson-Boltzmann equation. © 1995, Khayyam Publishing.