Boltzmann Model for viscoelastic particles: asymptotic behavior, pointwise lower bounds and regularity
Analysis of PDEs
2015-06-16 v2
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.
Cite
@article{arxiv.1306.1379,
title = {Boltzmann Model for viscoelastic particles: asymptotic behavior, pointwise lower bounds and regularity},
author = {Ricardo J. Alonso and Bertrand Lods},
journal= {arXiv preprint arXiv:1306.1379},
year = {2015}
}
Comments
A new scaling is proposed in this new version. It allows to by-pass the proof of the convergence of the energy performed in the previous version. The convergence is now obtained 'only' thanks to the dissipation of entropy functional