The dissipative linear Boltzmann equation for hard spheres
arXiv:cond-mat/0312524 · doi:10.1007/s10955-004-2267-7
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