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arXiv · 0712.0124

Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media

Stéphane Mischler·Clément Mouhot
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Abstract

We consider a space-homogeneous gas of {\it inelastic hard spheres}, with a {\it diffusive term} representing a random background forcing (in the framework of so-called {\em constant normal restitution coefficients} $α\in [0,1]$ for the inelasticity). In the physical regime of a small inelasticity (that is $α\in [α_*,1)$ for some constructive $α_* \in [0,1)$) we prove uniqueness of the stationary solution for given values of the restitution coefficient $α\in [α_*,1)$, the mass and the momentum, and we give various results on the linear stability and nonlinear stability of this stationary solution.

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Stéphane Mischler, Clément Mouhot. 2007-12-02. Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media. https://doi.org/10.3934/dcds.2009.24.159

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