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Kinetic Wedge Layers and Diffusive Limit of Neutron Transport in Polygonal Domains

  • Zhimeng Ouyang
  • Lei Wu
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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∞. 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 L2 diffusive limit at rate O(ε1/2) on general bounded simple polygons, including those with reentrant vertices.

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Cite

BibTeXRIS
BibTeX
@misc{ouyang2026kinetic,
  title = {{Kinetic Wedge Layers and Diffusive Limit of Neutron Transport in Polygonal Domains}},
  author = {Zhimeng Ouyang and Lei Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.00698},
  eprint = {2609.00698},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00698},
}
RIS
TY  - UNPB
TI  - Kinetic Wedge Layers and Diffusive Limit of Neutron Transport in Polygonal Domains
AU  - Zhimeng Ouyang
AU  - Lei Wu
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.00698
UR  - https://arxiv.org/abs/2609.00698
AB  - 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^∞. 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(ε^1/2) on general bounded simple polygons, including those with reentrant vertices.
ER  -