Boundary Layer of Transport Equation with In-Flow Boundary

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.