Validation of a kinetic-type equation for slowing particles in random media

We present a microscopic model for slowing particles in a random inhomo- geneous medium, where the inhomogeneities consist in spherical obstacles with Poisson dis- tributed centres. We study the asymptotic behaviour of the particle system when the radius of the obstacles vanishes and their density grows to infinity in such a way that the mean free path of the particles stays finite, while the slowing rate grows to infinity so that the loss of kinetic energy of the particles at each crossing is of order 1. We derive, in this asymptotics, the associated kinetic type limit equation for the proba- bility measure of the slowing particles, which includes a term proportional to a Dirac delta measure in v = 0 which guarantees the conservation of mass. The work is in collaboration with A.J. Soares and F. Golse.