Boltzmann Model for viscoelastic particles: asymptotic behavior, pointwise lower bounds and regularity

TL;DR

This paper analyzes the long-term behavior of viscoelastic particles using the Boltzmann equation, establishing convergence to a Maxwellian state, with bounds and regularity results generalizing classical models.

Contribution

It provides new results on the asymptotic behavior, lower bounds, and regularity for viscoelastic particles, extending classical models to more general cases.

Findings

Existence of a universal Maxwellian asymptotic state

Explicit convergence rate towards the Maxwellian

Exponential lower bounds and propagation of regularity

Abstract

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 and explicit the rate of convergence towards it. Exponential lower pointwise bounds and propagation of regularity are also studied. These results can be seen as the generalization of several classical facts holding for the pseudo-Maxwellian and constant normal restitution models.