The dissipative linear Boltzmann equation for hard spheres

Abstract

We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The equilibrium state is a universal Maxwellian distribution function with the same velocity as field particles and with a non--zero temperature lower than the background one, which depends on the details of the binary collision. Thanks to the H--theorem we then prove strong convergence of the solution to the Boltzmann equation towards the equilibrium.

17 pages, submitted to Journal of Statistical Physics

References in corpus (2)

• Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions
• Scaling Solutions of Inelastic Boltzmann Equations with Over-populated High Energy Tails

Cited by in corpus (5)

• Integral representation of the linear Boltzmann operator for granular gas dynamics with applications
• Entropy dissipation estimates for the linear Boltzmann operator
• Equilibrium Solution to the Inelastic Boltzmann Equation Driven by a Particles Thermal Bath
• Spectral analysis of transport equations with bounce-back boundary conditions
• Long time behavior of non-autonomous Fokker-Planck equations and the cooling of granular gases