Workshop - Problèmes mathématiques et modélisation en théorie cinétique

Thierry Goudon

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 exponential rate.

This is the object of joint works with A. Vavasseur (UNS) and R. Alonso (PUC, Rio).

Partenaires

Irmar LMJL ENS Rennes LMBA LAREMA

Tutelles

ANR CNRS Rennes 1 Rennes 2 Nantes INSA Rennes INRIA ENSRennes UBO UBS Angers UBL