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

Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains Consider the steady neutron transport equation with diffusive boundary condition. In Wu and Guo (Commun Math Phys 336:1473–1553, 2015) and Wu et al. (J Stat Phys 165:585–644, 2016), 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 the diffusive limit for a 2D convex domain. Our contribution relies on novel weighted $${W^{1,\infty}}$$ W 1 , ∞ estimates for the Milne problem with geometric correction in the presence of a convex domain, as well as an $${L^{2m}-L^{\infty}}$$ L 2 m - L ∞ framework which yields stronger remainder estimates. Archive for Rational Mechanics and Analysis Springer Journals

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

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Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
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