We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, 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 close-to-equilibrium regime. We also study the long-time behaviour of these solutions and prove a convergence to equilibrium with an exponential rate.
- Pub Date:
- January 2020
- Mathematics - Analysis of PDEs;
- Mathematical Physics
- 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