Abstract
We consider the diffusive limit of a steady neutron transport equation with one-speed velocity in a two-dimensional annulus. A classical theorem in Bensoussan et al. (Publ Res Inst Math Sci 15:53–157, 1979) states that the solution can be approximated in $$L^{\infty }$$ by the sum of the interior solution and Knudsen layer derived from Milne problem. However, this result was disproved in Wu and Guo (Commun Math Phys 336:1473–1553, 2015) in a plate via a different boundary layer expansion with geometric correction. In this paper, we established the diffusive limit and provide a counterexample to Bensoussan et al. (1979) in non-convex domains.
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