PENCIL-BEAM APPROXIMATION OF STATIONARY FOKKER-PLANCK

被引：3
作者：
Bal, Guillaume [1 ,2 ]
Palacios, Benjamin [1 ,2 ]
机构：
[1] Univ Chicago, Dept Stat, Chicago, IL 60637 USA
[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2020年 / 52卷 / 04期
基金：
美国国家科学基金会;
关键词：
Fokker-Planck; Fermi pencil-beam; narrow beam; Wasserstein distance; EQUATION; STABILITY;
D O I：
10.1137/19M1295775
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Solutions of stationary Fokker-Planck equations in the narrow beam regime are commonly approximated by either ballistic linear transport or a Fermi pencil-beam equation. We present a rigorous approximation analysis of these three models in a half-space geometry. Error estimates are obtained in a 1-Wasserstein sense, which is an adapted metric to quantify beam spreading. The required well-posedness and regularity results for the stationary Fokker-Planck equation with singular internal and boundary sources are also presented in detail.
引用
收藏
页码：3487 / 3519
页数：33
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