Macroscopic limit of Vlasov type equations with friction

The purpose of this paper is to investigate the limit of some kinetic equat ions with a strong force. Due to friction, the solution concentrates to a m onokinetic distribution so as to keep the total of force bounded and in the limit we recover a macroscopic system. This kind of asymptotics is a natur al question when the mass of the particles is very small or their inertia i s neglected. After that we also study the properties of the limit system an d especially the uniqueness of solutions which provides the full convergenc e of the family of solutions to the kinetic equation. (C) 2000 Editions sci entifiques et medicales Elsevier SAS.