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Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation

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Abstract

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.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI, 02912, USA

    Lei Wu & Yan Guo

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  1. Lei Wu
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  2. Yan Guo
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Correspondence to Yan Guo.

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Communicated by C. Mouhot

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Wu, L., Guo, Y. Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation. Commun. Math. Phys. 336, 1473–1553 (2015). https://doi.org/10.1007/s00220-015-2315-y

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  • DOI: https://doi.org/10.1007/s00220-015-2315-y

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