# A free boundary problem in kinetic theory

# A free boundary problem in kinetic theory

We consider a rigid body colliding with a continuum of particles. We assume that the body is moving at a velocity close to an equilibrium velocity V_{infty} and that the particles colliding with the body reflect probabilistically with some probablility distribution K. The fact that the particles and the body might collide many times or even infinitely many times makes the problem highly nontrivial even we only consider simple cases. We prove that the system does tend to an equilibrium. Moreover, we find a condition that is sufficient and almost necessary that the collective force of the colliding particles reverses the relative velocity V(t) of the body, that is, changes the sign of V(t)-V_{infty}, before the body approaches equilibrium. Examples of both reversal and irreversal are given.