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Half-space kinetic equations with general boundary conditions


Authors: Qin Li, Jianfeng Lu and Weiran Sun
Journal: Math. Comp. 86 (2017), 1269-1301
MSC (2010): Primary 35Q20; Secondary 65N35
DOI: https://doi.org/10.1090/mcom/3155
Published electronically: October 12, 2016
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Abstract: We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various types of reflections, extending our previous work on half-space equations with incoming boundary conditions. As in our previous work, the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.


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Additional Information

Qin Li
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53705
Email: qinli@math.wisc.edu

Jianfeng Lu
Affiliation: Departments of Mathematics, Physics, and Chemistry, Duke University, Box 90320, Durham, North Carolina 27708
Email: jianfeng@math.duke.edu

Weiran Sun
Affiliation: Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada

DOI: https://doi.org/10.1090/mcom/3155
Received by editor(s): September 9, 2015
Received by editor(s) in revised form: December 2, 2015
Published electronically: October 12, 2016
Additional Notes: The research of the first author was supported in part by the AFOSR MURI grant FA9550-09-1-0613 and the National Science Foundation under award DMS-1318377
The research of the second author was supported in part by the Alfred P. Sloan Foundation and the National Science Foundation under award DMS-1312659 and DMS-1454939
The research of the third author was supported in part by the Simon Fraser University President’s Research Start-up Grant PRSG-877723 and NSERC Discovery Individual Grant #611626
Article copyright: © Copyright 2016 American Mathematical Society