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

@article{Bobylev2001ErratumO, 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}, year={2001}, volume={103}, pages={1137-1138} }

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

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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…

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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

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- 2010

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…

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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.

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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

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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

- PhysicsSIAM J. Math. Anal.
- 2012

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

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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…

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

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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.

## References

### On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions

- Mathematics, Physics
- 2000

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…