Inelastic Boltzmann Equation Driven by a Particle Thermal Bath

Rafael Sanabria

Inelastic Boltzmann Equation Driven by a Particle Thermal Bath

Analysis of PDEs 2020-08-17 v2 Mathematical Physics math.MP

Authors: Rafael Sanabria

Abstract

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.

Keywords

boltzmann equation heat equation partial differential equations

Cite

@article{arxiv.2002.02811,
  title  = {Inelastic Boltzmann Equation Driven by a Particle Thermal Bath},
  author = {Rafael Sanabria},
  journal= {arXiv preprint arXiv:2002.02811},
  year   = {2020}
}

Comments

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

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