Validity and regularization of classical half-space equations

Abstract

Recent result [Wu and Guo, Comm. Math. Phys., 2015] has shown that over the 2D unit disk, the classical half-space equation (CHS) for the neutron transport does not capture the correct boundary layer behaviour as long believed. In this paper we develop a regularization technique for CHS to any arbitrary order and use its first-order regularization to show that in the case of the 2D unit disk, although CHS misrepresents the boundary layer behaviour, it does give the correct boundary condition for the interior macroscopic (Laplace) equation. Therefore CHS is still a valid equation to recover the correct boundary condition for the interior Laplace equation over the 2D unit disk.

References in corpus (4)

• Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation
• Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains
• Implicit Asymptotic Preserving Method for Linear Transport Equations
• Asymptotic Analysis of Transport Equation in Annulus

Cited by in corpus (8)

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• Stability of Stationary Inverse Transport Equation in Diffusion Scaling
• Boundary Layer of Transport Equation with In-Flow Boundary
• Inverse problems for the stationary transport equation in the diffusion scaling
• Asymptotic Analysis of Transport Equation in Bounded Domains
• Random Sampling and Efficient Algorithms for Multiscale PDEs
• Generalized multiscale finite element method for the steady state linear Boltzmann equation
• A low-rank Schwarz method for radiative transport equation with heterogeneous scattering coefficient