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Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media. (English) Zbl 1160.76042
Summary: 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 momentum, and we give various results on linear and nonlinear stability of this stationary solution.

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76T25 Granular flows
74E30 Composite and mixture properties
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