On some related non homogeneous 3D Boltzmann models in the non cutoff case
type: Item
instance of: scholarly article
title: On some related non homogeneous 3D Boltzmann models in the non cutoff case
zbMATH Open document ID: 0983.35034
author: Radjesvarane Alexandre
published in: Journal of Mathematics of Kyoto University
publication date: 2002-04-09T00:00:00Z
review text: The aim of this paper is to study the following three models: modified Boltzmann equation, generalized Boltzmann equation, and the Dirac Boltzmann model. The models are non-homogeneous, and the collision operator cannot be splitted into the usual gain and loss terms in view of the high singularity of the collision cross sections. The analysis is performed without assuming Grad's angular cutoff hypothesis on the cross sections. In the modified Boltzmann model the collision operator is regularized by dividing the zero moment of the solution, and the author proves existence results in the distribution sense. Then the existence of a weak solution is proved for the Dirac Boltzmann model. The final chapter of the paper deals with the collision operator (generalized Boltzmann operator), which is represented as an integral of usual Boltzmann collision term. In all the cases the author mollifies the collision kernel in the neighborhood of approximately equal velocities.
reviewed by: P. B. Dubovski
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 82B40
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35K70
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 1590229
zbMATH Keywords: modified Boltzmann equation
zbMATH Keywords: generalized Boltzmann equation
zbMATH Keywords: Dirac Boltzmann model
zbMATH Keywords: high singularity of the collision cross sections
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250517678
OpenAlex ID: W1512568094
DOI: 10.1215/KJM/1250517678
description: scientific article; zbMATH DE number 1590229