Diffusive Limit with Geometric Correction of Unsteady Neutron Transport Equation
Analysis of PDEs
2016-05-06 v3
Abstract
We consider the diffusive limit of an unsteady neutron transport equation in a two-dimensional plate with one-speed velocity. We show the solution can be approximated by the sum of interior solution, initial layer, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory in \cite{Bensoussan.Lions.Papanicolaou1979} which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.
Keywords
Cite
@article{arxiv.1509.07699,
title = {Diffusive Limit with Geometric Correction of Unsteady Neutron Transport Equation},
author = {Lei Wu},
journal= {arXiv preprint arXiv:1509.07699},
year = {2016}
}
Comments
34 pages. arXiv admin note: substantial text overlap with arXiv:1404.2583