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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2009

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

Résumé

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} $\alpha \in [0,1]$ for the inelasticity). In the physical regime of a small inelasticity (that is $\alpha \in [\alpha_*,1)$ for some constructive $\alpha_* \in [0,1)$) we prove uniqueness of the stationary solution for given values of the restitution coefficient $\alpha \in [\alpha_*,1)$, 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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Dates et versions

hal-00193200 , version 1 (01-12-2007)

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Stéphane Mischler, Clément Mouhot. Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media. Discrete and Continuous Dynamical Systems - Series A, 2009, 24 (1), pp.159-185. ⟨10.3934/dcds.2009.24.159⟩. ⟨hal-00193200⟩
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