Publication 16-CNA-008

Geometric Correction In Diffusive Limit Of Neutron Transport Equation In 2D Convex Domains

Yan Guo
Division of Applied Mathematics
Brown University
Providence, RI 02912, USA
guoy@dam.brown.edu

Lei Wu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
lwu2@andrew.cmu.edu

Abstract: Consider the steady neutron transport equation with diffusive boundary condition. In [17] and [18], 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 weighted $W^{1,\infty}$ 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.

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