In 2001 L. Bruneau and S. De Bièvre introduced an original
model describing the interaction between a classical particle and an
oscillating media. For this model they showed (under some conditions)
that the media acts on the particle like a friction force. Here, I will
present results about the Vlasov-Wave equation : the kinetic equation
coming from their model.

Since in 2016 S. De bièvre, T. Goudon and A. Vavasseur showed that,
under an appropriate scaling, the Vlasov-Wave equation is asymptotic to
the attractive Vlasov-Poisson equation, it is natural to ask the
question of the Landau damping for this model. First, I will recall the
mechanisms of the Landau damping for the classical Vlasov equation and
then I will explain how these mechanisms are modified in the Vlasov-Wave
case. All these results will be illustrated by numerical simulations.