Diffusion approximation for the linear Boltzmann equation of semiconductor theory with analysis of the initial layer
type: Item
instance of: scholarly article
title: Diffusion approximation for the linear Boltzmann equation of semiconductor theory with analysis of the initial layer
zbMATH Open document ID: 0879.35146
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-04-29T00:00:00Z
review text: The author considers the relation between the linear Boltzmann equation and the corresponding hydrodynamic approximation and shows that the latter is the diffusion equation. Two cases are discussed in the consideration of the initial layer when considering the Boltzmann equation for charged particles, one corresponding to a relatively weak external field and the other when the field and the collisions are of the same order of magnitude. A general theory is obtained for the bound of errors in the approximations used, and a condition is developed for the diffusion constant to be positive. There is no illustration of how the abstract ideas considered can be used in any physical situation.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A35
Mathematics Subject Classification ID: 76P05
zbMATH DE Number: 1005710
zbMATH Keywords: linear Boltzmann equation
zbMATH Keywords: hydrodynamic approximation
zbMATH Keywords: diffusion equation
author: Jacek Banasiak
reviewed by: Ll. G. Chambers
MaRDI profile type: Publication
full work available at URL: jmaa.1996.5164
OpenAlex ID: W2092055779
Wikidata QID: Q72545568
cites work: The Cauchy problem for the linear Maxwell-Boltzmann equation
cites work: Q4843344
cites work: Asymptotic Analysis of Abstract Linear Kinetic Equations
cites work: ASYMPTOTIC ANALYSIS OF THE FOKKER-PLANCK EQUATION RELATED TO BROWNIAN MOTION
cites work: Diffusion limit for the linear boltzmann equation of the neutron transport theory
cites work: Diffusion Approximation and Computation of the Critical Size
cites work: Existence of solutions and diffusion approximation for a model Fokker-Planck equation
cites work: Conditions for runaway phenomena in the kinetic theory of particle swarms
cites work: New asymptotic expansion algorithm for singularly perturbed evolution equations
cites work: ASYMPTOTIC ANALYSIS OF A MODEL KINETIC EQUATION
cites work: Q4857772
cites work: One-parameter semigroups of positive operators
cites work: Q4009097
cites work: Runaway Phenomena and Fluid Approximation Under High Fields in Semiconductor Kinetic Theory
cites work: On Positive Contractions In L p -Spaces
DOI: 10.1006/JMAA.1996.5164
description: scientific article; zbMATH DE number 1005710