Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains

Abstract

Consider the steady neutron transport equation with diffusive boundary condition. In [Wu and Guo(2015) Comm. Math. Phys.] and [Wu and Yang and Guo(2016) Preprint], it was discovered that geometric correction is necessary for the Milne problem of Knudsen-layer construction in a disk or annulus. In this paper, we establish diffusive limit for a 2D convex domain. Our contribution relies on novel $W^{1,\infty }$ estimates for the Milne problem with geometric correction in the presence of a convex domain, as well as an $L^{2m}-L^{\infty }$ framework which yields stronger remainder estimates.

60 pages

References in corpus (3)

• Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation
• Asymptotic Analysis of Transport Equation in Annulus
• Half-space Kinetic Equations with General Boundary Conditions

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