The diffusion approximation of the Boltzmann equation of Maxwellian molecules
type: Item
instance of: scholarly article
title: The diffusion approximation of the Boltzmann equation of Maxwellian molecules
zbMATH Open document ID: 0536.60098
author: Tadahisa Funaki
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1983-01-01T00:00:00Z
review text: The Landau equation describes the evolution of the one-particle density of a weakly coupled gas resp. a plasma. In contrast to the Boltzmann equation it has been studied rigorously only to a small extent. In this paper the Landau equation is derived as the diffusion limit of the Boltzmann equation. In this limit the collision rate increases and the change of velocities decreases in a diffusive scaling. This goes back to the original idea of Landau. It is proved that the corresponding semigroups converge in a suitable sense. The proof uses jump type Markov processes associated with the Boltzmann equation and a diffusion process associated with the Landau equation by showing their corresponding convergence. In two final chapters the time evolution of moments and trend to equilbrium is treated and a one-dimensional analogous model is studied.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 3852184
zbMATH Keywords: Landau equation
zbMATH Keywords: Boltzmann equation
zbMATH Keywords: convergence of semigroups
zbMATH Keywords: associated Markov processes
zbMATH Keywords: diffusion limit
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195182454
OpenAlex ID: W2023493773
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DOI: 10.2977/PRIMS/1195182454
description: scientific article; zbMATH DE number 3852184