Asymptotic Analysis of Unsteady Neutron Transport Equation

TL;DR

This paper rigorously analyzes the diffusive limit of the unsteady neutron transport equation in 2D convex domains, addressing boundary layer regularity issues through advanced asymptotic and functional analysis techniques.

Contribution

It introduces a novel asymptotic expansion method with boundary layer corrections for the unsteady neutron transport equation, overcoming regularity challenges.

Findings

Established the diffusive limit with initial and boundary layer corrections.

Developed an $L^{2m}-L^{inity}$ framework for stronger remainder estimates.

Provided detailed asymptotic analysis inspired by compatibility conditions.

Abstract

Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity in the boundary layer with geometric correction. Our contribution relies on a detailed analysis of asymptotic expansions inspired by the compatibility condition and an intricate $L^{2m}-L^{\infty}$ framework which yields stronger remainder estimates.