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Boundary Layer of Transport Equation with In-Flow Boundary

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Abstract

Consider the steady neutron transport equation in two dimensional convex domains with an in-flow boundary condition. We establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition of boundary data to separate the regular and singular boundary layers, novel weighted \(W^{1,\infty }\) estimates for the Milne problem with geometric correction in convex domains, and an \(L^{2m}-L^{\infty }\) framework which yields stronger remainder estimates.

Notes

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA

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