On the Boltzmann equation for diffusively excited granular media
IM Gamba, V Panferov, C Villani - Communications in Mathematical …, 2004 - Springer
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres,
with a diffusive term representing a random background forcing. Under the assumption that …
with a diffusive term representing a random background forcing. Under the assumption that …
[PDF][PDF] Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
JA Carrillo, G Toscani - Riv. Mat. Univ. Parma, 2007 - mate.unipv.it
The present notes are intended to present a detailed review of the existing results in
dissipative kinetic theory which make use of the contraction properties of two main families …
dissipative kinetic theory which make use of the contraction properties of two main families …
Existence of global solutions to the Cauchy problem for the inelastic Boltzmann equation with near-vacuum data
RJ Alonso - Indiana University mathematics journal, 2009 - JSTOR
The Cauchy problem for the inelastic Boltzmann equation is studied for small data.
Existence and uniqueness of mild and weak solutions are obtained for sufficiently small data …
Existence and uniqueness of mild and weak solutions are obtained for sufficiently small data …
Contractive Metrics for a Boltzmann equation for granular gases: Diffusive equilibria
M Bisi, JA Carrillo, G Toscani - Journal of statistical physics, 2005 - Springer
We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic
thermostat by means of the contractivity of a suitable metric in the set of probability …
thermostat by means of the contractivity of a suitable metric in the set of probability …
Sonine approximation for collisional moments of granular gases of inelastic rough spheres
A Santos, GM Kremer, M dos Santos - Physics of Fluids, 2011 - pubs.aip.org
We consider a dilute granular gas of hard spheres colliding inelastically with coefficients of
normal and tangential restitution α and β, respectively. The basic quantities characterizing …
normal and tangential restitution α and β, respectively. The basic quantities characterizing …
Tanaka theorem for inelastic Maxwell models
F Bolley, JA Carrillo - Communications in mathematical physics, 2007 - Springer
We show that the Euclidean Wasserstein distance is contractive for inelastic homogeneous
Boltzmann kinetic equations in the Maxwellian approximation and its associated Kac-like …
Boltzmann kinetic equations in the Maxwellian approximation and its associated Kac-like …
Direct simulation of the uniformly heated granular Boltzmann equation
IM Gamba, S Rjasanow, W Wagner - Mathematical and computer modelling, 2005 - Elsevier
In this paper, we study properties of dilute granular flows, which are described by the
spatially homogeneous uniformly heated inelastic Boltzmann equation. A new modification …
spatially homogeneous uniformly heated inelastic Boltzmann equation. A new modification …
Kinetic models with randomly perturbed binary collisions
F Bassetti, L Ladelli, G Toscani - Journal of Statistical Physics, 2011 - Springer
We introduce a class of Kac-like kinetic equations on the real line, with general random
collisional rules which, in some special cases, identify models for granular gases with a …
collisional rules which, in some special cases, identify models for granular gases with a …
L1 and BV-type stability of the inelastic Boltzmann equation near vacuum
Z Wu - Continuum Mechanics and Thermodynamics, 2010 - Springer
The L 1 and BV-type stability to mild solutions of the inelastic Boltzmann equation is given in
this paper. The result is an extension of the stability of the classical solution of the elastic …
this paper. The result is an extension of the stability of the classical solution of the elastic …
Global existence and stability of mild solutions to the inelastic Boltzmann system for gas mixtures
SY Ha, SE Noh - Quarterly of applied mathematics, 2010 - ams.org
We study the global existence and uniform stability estimate of mild solutions to the inelastic
Boltzmann system for gas mixtures, when initial data are small and decay exponentially in …
Boltzmann system for gas mixtures, when initial data are small and decay exponentially in …