Abstract

It is a standard assumption in kinetic transport theory that collision processes are instantaneous. We shall report on the initiation of a research program, where this idealization is lifted. The idea for modeling binary, non-instantaneous collisions is to replace instantaneous jumps in the state space of a pair of particles by continuous processes taking finite time. The duration of the collision process can be deterministic or stochastic. This results in a system of equations for the particle distribution between collisions and for the distribution of particle pairs during collision processes. Results will be presented on two spatially homogeneous models for non-instantaneous alignment collisions, where in one case the collision time is governed by a simple Poisson process, whereas in the other case collisions end after reaching complete alignment in finite time. For both models existence, long-time behavior, and the instantaneous limit towards a standard kinetic model will be discussed.(joint work with Laura Kanzler and Veronica Tora)