Volume 31, Issue 2
Diffusion Limit of 1-D Small Mean Free Path of Radiative Transfer Equations in Bounded Domain

J. Part. Diff. Eq., 31 (2018), pp. 177-192.

Published online: 2018-07

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• Abstract

In this paper, we consider the diffusion limit of the small mean free path for the radiative transfer equations, which describe the spatial transport of radiation in material. By using asymptotic expansions, we prove that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero, and moreover we study the boundary layer problem and mixed layer problem in bounded domain [0,1]. Then we show the validity of their asymptotic expansions relies only on the smoothness of boundary condition, and remove the Fredholm alternative and centering condition.

• Keywords

Transfer equations asymptotic analysis diffusion limit boundary layer mixed layer.

34E05, 76D10, 76D99

wangshu@bjut.edu.cn (Shu Wang)

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@Article{JPDE-31-177, author = {Chen , Xiao and Wang , Shu}, title = {Diffusion Limit of 1-D Small Mean Free Path of Radiative Transfer Equations in Bounded Domain}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {2}, pages = {177--192}, abstract = {

In this paper, we consider the diffusion limit of the small mean free path for the radiative transfer equations, which describe the spatial transport of radiation in material. By using asymptotic expansions, we prove that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero, and moreover we study the boundary layer problem and mixed layer problem in bounded domain [0,1]. Then we show the validity of their asymptotic expansions relies only on the smoothness of boundary condition, and remove the Fredholm alternative and centering condition.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n2.4}, url = {http://global-sci.org/intro/article_detail/jpde/12516.html} }
TY - JOUR T1 - Diffusion Limit of 1-D Small Mean Free Path of Radiative Transfer Equations in Bounded Domain AU - Chen , Xiao AU - Wang , Shu JO - Journal of Partial Differential Equations VL - 2 SP - 177 EP - 192 PY - 2018 DA - 2018/07 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n2.4 UR - https://global-sci.org/intro/article_detail/jpde/12516.html KW - Transfer equations KW - asymptotic analysis KW - diffusion limit KW - boundary layer KW - mixed layer. AB -

In this paper, we consider the diffusion limit of the small mean free path for the radiative transfer equations, which describe the spatial transport of radiation in material. By using asymptotic expansions, we prove that the nonlinear transfer equation has a diffusion limit as the mean free path tends to zero, and moreover we study the boundary layer problem and mixed layer problem in bounded domain [0,1]. Then we show the validity of their asymptotic expansions relies only on the smoothness of boundary condition, and remove the Fredholm alternative and centering condition.

Xiao Chen & Shu Wang. (2019). Diffusion Limit of 1-D Small Mean Free Path of Radiative Transfer Equations in Bounded Domain. Journal of Partial Differential Equations. 31 (2). 177-192. doi:10.4208/jpde.v31.n2.4
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