Diffusion approximation and computation of the critical size-Reference-Cited by-同舟云学术

Diffusion approximation and computation of the critical size

Published:1984 Issue:2 Volume:284 Page:617-649
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Bardos C.,Santos R.,Sentis R.

Abstract

This paper is devoted to the mathematical definition of the extrapolation length which appears in the diffusion approximation. To obtain this result, we describe the spectral properties of the transport equation and we show how the diffusion approximation is related to the computation of the critical size. The paper also contains some simple numerical examples and some new results for the Milne problem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1984-284-02/S0002-9947-1984-0743736-0/S0002-9947-1984-0743736-0.pdf

Reference21 articles.

1. On the spectrum of neutron transport equation in finite bodies;Albertoni, S.;J. Math. Anal. Appl.,1966

2. Nonlinear operators in ordered Banach spaces and some applications to nonlinear boundary value problems;Amann, Herbert,1976

3. Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d’approximation; application à l’équation de transport;Bardos, Claude;Ann. Sci. \'{E}cole Norm. Sup. (4),1970

4. Boundary layers and homogenization of transport processes;Bensoussan, Alain;Publ. Res. Inst. Math. Sci.,1979

5. Stability and control of stochastic systems with wide-band noise disturbances. I;Blankenship, G.;SIAM J. Appl. Math.,1978

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