Pencil-beam approximation of stationary Fokker-Planck
Analysis of PDEs
2020-06-09 v2
Abstract
Solutions of stationary Fokker-Planck equations in the narrow beam regime are commonly approximated by either ballistic linear transport or by 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.
Keywords
Cite
@article{arxiv.1910.12150,
title = {Pencil-beam approximation of stationary Fokker-Planck},
author = {Guillaume Bal and Benjamin Palacios},
journal= {arXiv preprint arXiv:1910.12150},
year = {2020}
}