Stationary states of a gas in a radiation field from a kinetic point of view
type: Item
instance of: scholarly article
title: Stationary states of a gas in a radiation field from a kinetic point of view
zbMATH Open document ID: 1006.82026
author: Anne Nouri
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2003-03-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73551
review text: The solutions of the kinetic equation for the distribution function of the photons and Boltzmann equations for two types of the gas spices are studied analytically. The stationary solution in the slab geometry is considered. Particles of the gas that are populating the two fundamental levels are taken into account. The kinetic equation for the distribution function of the photons includes effects of absorption, spontaneous and stimulated emissions. The Boltzmann equations for distribution functions of two types of gas spices include effects of absorption, spontaneous and stimulated emissions and elastic collisions. The one-dimensional problem is considered when photons are emitted perpendicular to the walls of the channel and the relativistic effects are negligibly small. Existence of the stationary solutions of kinetic equations is proofed analytically. The main result of the paper is based on several proofed lemmas and a theorem.
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 82D05
Mathematics Subject Classification ID: 85A25
zbMATH DE Number: 1796100
zbMATH Keywords: kinetic equation
zbMATH Keywords: distribution function
zbMATH Keywords: photons
zbMATH Keywords: Boltzmann equations
zbMATH Keywords: gas
zbMATH Keywords: stationary solution
zbMATH Keywords: slab geometry
reviewed by: Oleg A. Sinkevich
MaRDI profile type: Publication
OpenAlex ID: W2323350114
cites work: Q4705757
cites work: The nonaccretive radiative transfer equations: Existence of solutions and Rosseland approximation
cites work: Q5616800
cites work: The Boltzmann equation and its applications
cites work: On the Cauchy problem for Boltzmann equations: Global existence and weak stability
cites work: Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II
cites work: Kinetic theory of atoms and photons: An application to the Milne-Chandrasekhar problem
cites work: Kinetic approach for two-level atoms interacting with monochromatic photons
DOI: 10.5802/AFST.996
description: scientific article; zbMATH DE number 1796100