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

Abstract

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 $\alpha \in [{\alpha }_{\ast },1)$ for some constructive ${\alpha }_{\ast }\in [0,1)$) we prove uniqueness of the stationary solution for given values of the restitution coefficient $\alpha \in [{\alpha }_{\ast },1)$, the mass and the momentum, and we give various results on the linear stability and nonlinear stability of this stationary solution.

References in corpus (4)

• Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions
• On the Boltzmann equation for diffusively excited granular media
• Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem
• Cooling process for inelastic Boltzmann equations for hard spheres, Part II: Self-similar solutions and tail behavior

Cited by in corpus (5)

• Factorization for non-symmetric operators and exponential H-theorem
• Boltzmann Model for viscoelastic particles: asymptotic behavior, pointwise lower bounds and regularity
• Fractional Fokker-Planck Equation with General Confinement Force
• A Spectral Study of the Linearized Boltzmann Equation for Diffusively Excited Granular Media
• Uniqueness in the weakly inelastic regime of the equilibrium state of the inelastic Boltzmann equation driven by a particle bath