The dissipative linear Boltzmann equation for hard spheres

Details The dissipative linear Boltzmann equation for hard spheres The dissipative linear Boltzmann equation for hard spheres

2003-12-19

arxiv.org/abs/cond-mat/0312524v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, submitted to Journal of Statistical Physics

Scientific paper

10.1007/s10955-004-2267-7

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.

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