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Article Contents

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

• We consider a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing (in the framework of so-called 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.
Mathematics Subject Classification: Primary: 76P05; Secondary: 76T25.

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