Erratum on “On Some Properties of Kinetic and Hydrodynamic Equations for Ineleastic Interactions”

  title={Erratum on “On Some Properties of Kinetic and Hydrodynamic Equations for Ineleastic Interactions”},
  author={Alexander V. Bobylev and Jos{\'e} A. Carrillo and Irene M. Gamba},
  journal={Journal of Statistical Physics},
This note corrects the strong form of the pseudo-Maxwellian collision integral given in ref. 1. The correction does not change main results of ref. 1 (Sections 3–8) based on the weak form of the integral. More precisely , it relates to the Boltzmann equation in strong form written after (2.8) and (2.10) in ref. 1. The identity (2.10) should read Q(f, f)= 1 4p F R 3 F S 2 [f(t, v g) f(t, w g) J−f(t, v) f(t, w)] dn dw (1) where v g , w g are the pre-collisional velocities given by v g = 1 2 (v+w… 
11 Citations

The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres

We study a generic class of inelastic soft sphere models with a binary collision rate g^ν that depends on the relative velocity g. This includes previously studied inelastic hard spheres (ν = 1) and

Self-Similar Asymptotics for the Boltzmann Equation with Inelastic and Elastic Interactions

We consider some questions related to the self-similar asymptotics in the kinetic theory of both elastic and inelastic particles. In the second case we have in mind granular materials, when the model

Dynamics and hydrodynamic limits of the inelastic Boltzmann equation

We investigate the macroscopic description of a dilute, gas-like system of particles, which interact through binary collisions that conserve momentum and mass, but which dissipate energy, as in the

One-Dimensional Dissipative Boltzmann Equation: Measure Solutions, Cooling Rate, and Self-Similar Profile

A dynamical fixed point theorem is applied on a suitable stable set, for the model dynamics, of Borel measures, of borel measures to prove the existence of a nontrivial self-similar profile after appropriate scaling of the Boltzmann equation.

Global solution to the inelastic Boltzmann equation with hard potentials

Some hypotheses of the restitution coefficient are made about the inelastic Boltzmann equation with hard potentials. It is shown that there exists a unique non-negative global solution to the Cauchy

Free Cooling and High-Energy Tails of Granular Gases with Variable Restitution Coefficient

We prove the so-called generalized Haff's law yielding the optimal algebraic cooling rate of the temperature of a granular gas described by the homogeneous Boltzmann equation for inelastic

Blow Up Analysis for Anomalous Granular Gases

This article investigates the long-time behavior of the solutions to the energy-dependent, spatially homogeneous, inelastic Boltzmann equation for hard spheres with and without drift term by introducing new strongly “nonlinear” self-similar variables.

Some alternative methods for hydrodynamic closures to dissipative kinetic models

Abstract Two different strategies for deriving hydrodynamic equations for dissipative kinetic models are presented and discussed. The homogeneity scaling approach, not very well-known in the physical

A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

(2 + 1) [XTpXpH12, CTH11]. + [Zuc11b]. 0 [Fed17]. 1 [BELP15, CAS11, Cor16, Fed17, GDL10, GBL16, Hau16, JV19, KT12, KM19c, Li19, MN14b, Nak17, Pal11, Pan14, RT14, RBS16b, RY12, SS18c, Sug10, dOP18]. 1

Recent development in kinetic theory of granular materials: analysis and numerical methods

This article aims to review recent mathematical results in kinetic granular materials, especially for those which arose since the last review by Villani, and discusses both theoretical and numerical developments.


On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions

We investigate a Boltzmann equation for inelastic scattering in which the relative velocity in the collision frequency is approximated by the thermal speed. The inelasticity is given by a velocity