Boltzmann Model for Viscoelastic Particles: Asymptotic Behavior, Pointwise Lower Bounds and Regularity

We investigate the long-time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state with explicit rate of convergence towards it. Exponential lower pointwise bounds and propagation of regularity are also studied. These results can be seen as a generalization of several classical results holding for the pseudo-Maxwellian and constant normal restitution models.