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

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
24
Number
1
Publisher
American Institute of Mathematical Sciences
Pages
159-185
Publication identifier
http://dx.doi.org/10.3934/dcds.2009.24.159
Metadata
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Author(s)
Mouhot, Clément
Mischler, Stéphane
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

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