Diffusive Limit with Geometric Correction of Unsteady Neutron Transport Equation

TL;DR

This paper investigates the diffusive limit of an unsteady neutron transport equation, introducing geometric corrections and challenging classical boundary layer theories with a counterexample.

Contribution

It provides a refined approximation of the solution including geometric corrections and constructs a counterexample to classical boundary layer descriptions.

Findings

Solution approximated by interior, initial, and boundary layers with geometric correction

Counterexample to classical boundary layer theory near boundaries

Refined understanding of neutron transport behavior in diffusive limits

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.