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Title: Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer
Authors: Kawagoe, Daisuke  kyouindb  KAKEN_id  orcid https://orcid.org/0000-0001-6419-5191 (unconfirmed)
Chen, I-Kun
Author's alias: 川越, 大輔
Keywords: Stationary transport equation
Boundary value problem
Discontinuity
Characteristic lines
Issue Date: Jan-2018
Publisher: Springer Nature
Journal title: Journal of Statistical Physics
Volume: 170
Issue: 1
Start page: 127
End page: 140
Abstract: We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result.
Rights: This is a post-peer-review, pre-copyedit version of an article published in Journal of Statistical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10955-017-1922-8.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
URI: http://hdl.handle.net/2433/242789
DOI(Published Version): 10.1007/s10955-017-1922-8
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