Inhomogeneous Ballistic Aggregation

The one-dimensional ballistic aggregation process is considered when the initial mass density or the initial particle velocities vanish outside of a finite or semi-infinite interval. In all cases, we compute the mass distributions in closed analytical form and study their long time asymptotics. The relevant length scales are found different (of the order t, t ^2/3, t ^1/2) if, at the initial time, particles occupy a finite (or semi-infinite) interval and if a finite (or infinite) number of them are set into motion.