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

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

2007-12-02

arxiv.org/abs/0712.0124v1

Discrete and Continuous Dynamical Systems: Series A 24, 1 (2009) 159-185

Mathematics

Analysis of PDEs

Scientific paper

10.3934/dcds.2009.24.159

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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