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Publication 145

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

Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA

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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