Inelastic Boltzmann Equation Driven by a Particle Thermal Bath

2020/01/17 by Sanabria, Rafael
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2002.02811

Abstract

We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient α∈(0,1), under the thermalization induced by a host medium with a fixed Maxwellian distribution and any fixed e∈(0,1]. When the restitution coefficient α 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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