Geometric correction for diffusive expansion of steady neutron transport equation
The authors revisit the diffusive limit of a steady one-velocity neutron transport equation in the two-dimensional unit disk. Two types of boundary conditions are considered, namely vacuum and diffusive. Well-posedness results for the transport equation along with \(L^2\) and \(L^\infty\) a priori estimates are derived. The Milne problem is studied in detail and \(L^2\) and \(L^\infty\) estimates are presented. Asymptotic analysis is performed by power type series expansion of the solution in a small parameter \(\epsilon\) (Knudsen number). It is shown that the error between the solution to the transport equation and the solution to a certain diffusion equation is \(O(\epsilon)\) in \(L^\infty\)-norm.
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