Inelastic Boltzmann Equation Driven by a Particle Thermal Bath
Abstract
We consider the spatially inhomogeneous Boltzmann equation for inelastic hardspheres, with constant restitution coefficient $\alpha\in(0,1)$, under the thermalization induced by a host medium with a fixed Maxwellian distribution and any fixed $e\in(0,1]$. When the restitution coefficient $\alpha$ is close to 1 we prove existence and uniqueness of global solutions considering the closetoequilibrium regime. We also study the longtime behaviour of these solutions and prove a convergence to equilibrium with an exponential rate.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2002.02811
 Bibcode:
 2020arXiv200202811S
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics
 EPrint:
 Improves the previous version for every restitution coefficient e. 42 pages, no figures. arXiv admin note: text overlap with arXiv:1311.5168, arXiv:1006.5523, arXiv:1106.2698 by other authors