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

Mouhot, Clément; Mischler, Stéphane

Mouhot, Clément; Mischler, Stéphane (2009), Stability, convergence to the steady state and elastic limit for the Boltzmann equation for diffusively excited granular media, Discrete and Continuous Dynamical Systems. Series A, 24, 1, p. 159-185. http://dx.doi.org/10.3934/dcds.2009.24.159

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00193200/en/

Date

2009

Journal name

Discrete and Continuous Dynamical Systems. Series A

Volume

Number

Publisher

American Institute of Mathematical Sciences

Pages

159-185

Abstract (EN)

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.

Subjects / Keywords

spectrum; degenerated perturbation; elastic limit; small inelasticity; stability; uniqueness; stationary solution; hard spheres; random forcing; inelastic Boltzmann equation; granular gases