Equilibrium Solution to the Inelastic Boltzmann Equation Driven by a Particles Thermal Bath

TL;DR

This paper proves the existence of smooth equilibrium solutions for the inelastic Boltzmann equation influenced by a thermal bath, using norm, moment, and regularity controls alongside dynamical methods.

Contribution

It introduces a novel approach to establish stationary solutions for the inelastic Boltzmann equation with thermalization effects.

Findings

Existence of smooth stationary solutions confirmed.

Controlled Lp-norms and moments ensure regularity.

Dynamical proof technique applied for solution existence.

Abstract

We show the existence of smooth stationary solutions for the inelastic Boltzmann equation under the thermalization induced by a host-medium with a fixed distribution. This is achieved by controlling the Lp-norms, the moments and the regularity of the solutions for the Cauchy problem together with arguments related to a dynamical proof for the existence of stationary states.