Year: 2026
Type: preprint
Abstract: We study the diffusive limit of the steady neutron transport equation with velocity-dependent in-flow boundary data in polygonal domains. On a bounded convex polygon, we construct an approximation by the interior solution, flat side layers, and wedge layers, and prove an algebraic error estimate in $L^\infty$. We also give a complete formulation and well-posedness theory for the kinetic wedge layer, including its algebraic decay. The proof combines a characteristic stability estimate, a weighted Mellin mapping theorem, a two-depth construction and matching scheme, and a shifted superharmonic barrier for the wedge corrector. We also prove the $L^2$ diffusive limit at rate $O(\varepsilon^{1/2})$ on general bounded simple polygons, including those with reentrant vertices.
Source: arXiv (Cornell University)
Authors: Ouyang, Zhimeng, Wu, Lei
Institutions: Lehigh University, Peking University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7206201311