PARTICLES INTERACTING WITH A VIBRATING MEDIUM: EXISTENCE OF SOLUTIONS AND CONVERGENCE TO THE VLASOV-POISSON SYSTEM

摘要

We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak solutions for a wide class of initial data and external forces. We also identify a relevant regime which allows us to derive, quite surprisingly, the attractive Vlasov-Poisson system from the coupled Vlasov wave equations.