Inelastic Boltzmann equation driven by a particle thermal bath

Rafael Sanabria

doi:10.3934/krm.2021018

Article Contents

2021, Volume 14, Issue 4: 639-679. Doi: 10.3934/krm.2021018

This issue Previous Article Incompressible Navier-Stokes-Fourier limit from the Landau equation Next Article Density dependent diffusion models for the interaction of particle ensembles with boundaries

Inelastic Boltzmann equation driven by a particle thermal bath

Rafael Sanabria^1, ,

Pontificia Universidade Católica do Rio de Janeiro¹, Gávea, Rio de Janeiro, 22451-900, Brazil

^* Corresponding author: Rafael Sanabria
^* Corresponding author: Rafael Sanabria

¹Research conducted while affiliated as a PhD. student at PUC-Rio

Received: August 31, 2020

Revised: March 31, 2021

Early access: June 2021

Published: August 2021

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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 fixed $ e\in(0,1] $ and a fixed Maxwellian distribution. 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.

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Mathematics Subject Classification: 76P05, 76T25, 47H20, 35Q35.

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