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 α ∈ [0, 1] for the inelasticity). In the physical regime of a small inelasticity (that is α ∈ [α∗, 1) for some constructive α∗ ∈ [0, 1)) we prove uniqueness of the stationary solution for given values of the restitution coefficient α ∈ [α∗, 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 (2000): 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05], 76T25 Granular flows [See also 74C99, 74E20].