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The dissipative linear Boltzmann equation for hard spheres

Bertrand Lods·Giuseppe Toscani
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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.

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Bertrand Lods, Giuseppe Toscani. 2003-12-19. The dissipative linear Boltzmann equation for hard spheres. https://doi.org/10.1007/s10955-004-2267-7

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