Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation

We revisit the diffusive limit of a steady neutron transport equation in a two-dimensional unit disk with one-speed velocity. A classical theorem by Bensoussan et al. (Publ Res Inst Math Sci 15(1):53–157, 1979) states that its solution can be approximated in L∞ by the leading order interior solution plus the Knudsen layer in the diffusive limit. In this paper, we construct a counterexample to this result via a different boundary layer expansion with geometric correction.