Geometric correction for diffusive expansion of steady neutron transport equation
type: Item
instance of: scholarly article
title: Geometric correction for diffusive expansion of steady neutron transport equation
zbMATH Open document ID: 1318.35128
author: Yanyan Li
published in: Communications in Mathematical Physics
publication date: 2015-04-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1404.2583
review text: The authors revisit the diffusive limit of a steady one-velocity neutron transport equation in the two-dimensional unit disk. Two types of boundary conditions are considered, namely vacuum and diffusive. Well-posedness results for the transport equation along with \(L^2\) and \(L^\infty\) a priori estimates are derived. The Milne problem is studied in detail and \(L^2\) and \(L^\infty\) estimates are presented. Asymptotic analysis is performed by power type series expansion of the solution in a small parameter \(\epsilon\) (Knudsen number). It is shown that the error between the solution to the transport equation and the solution to a certain diffusion equation is \(O(\epsilon)\) in \(L^\infty\)-norm.
reviewed by: Matthias Schlottbom
Mathematics Subject Classification ID: 35Q82
Mathematics Subject Classification ID: 82D75
zbMATH DE Number: 6424638
zbMATH Keywords: diffusion limit
zbMATH Keywords: Milne problem
zbMATH Keywords: boundary layer correction
MaRDI profile type: Publication
OpenAlex ID: W3104755947
arXiv ID: 1404.2583
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DOI: 10.1007/S00220-015-2315-Y
description: scientific article