Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains View Full Text


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Article Info

DATE

2017-05-30

AUTHORS

Yan Guo, Lei Wu

ABSTRACT

Consider the steady neutron transport equation with diffusive boundary condition. In Wu and Guo (Commun Math Phys 336:1473–1553, 2015) and Wu et al. (J Stat Phys 165:585–644, 2016), it was discovered that geometric correction is necessary for the Milne problem of Knudsen-layer construction in a disk or annulus. In this paper, we establish the diffusive limit for a 2D convex domain. Our contribution relies on novel weighted W1,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${W^{1,\infty}}$$\end{document} estimates for the Milne problem with geometric correction in the presence of a convex domain, as well as an L2m-L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^{2m}-L^{\infty}}$$\end{document} framework which yields stronger remainder estimates. More... »

PAGES

321-403

References to SciGraph publications

  • 2016-07-01. Regularity of the Boltzmann equation in convex domains in INVENTIONES MATHEMATICAE
  • 1994. The Mathematical Theory of Dilute Gases in NONE
  • <error retrieving object. in <ERROR RETRIEVING OBJECT
  • 2016-09-24. Asymptotic Analysis of Transport Equation in Annulus in JOURNAL OF STATISTICAL PHYSICS
  • 2015-02-25. Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s00205-017-1135-y

    DOI

    http://dx.doi.org/10.1007/s00205-017-1135-y

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