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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.

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