On a kinetic model for particles interacting with a vibrating medium
A couple of years ago, S. De Bievre initiated a research program
investigating the motion of a particle exchanging energy with a
vibrating medium. Both theoretical and numerical results bring out
remarkable phenomena: roughly speaking, the medium acts a a friction
force on the particles.
We revisit a part of the discussion in the framework of kinetic
equations, which leads to a coupled Vlasov-Wave system.
We will discuss some asymptotic issues showing, on the one hand, a
rather unexpected connection with the attractive Vlasov-Poisson system,
and, on the other hand, the asymptotic trend to equilibrium at
This is the object of joint works
with A. Vavasseur (UNS) and R. Alonso (PUC, Rio).