发表机构
Peking University; Lehigh University（北京大学; 利哈伊大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究建立了多边形域中带速度相关流入数据的定态中子输运方程的扩散极限，通过构造复合近似证明其收敛性，还给出动力学楔层的适定性理论，同时证明了简单多边形上$L^{2}$收敛的平方根速率结果。
AI 中文摘要
我们建立了多边形域中具有速度相关流入数据的定态中子输运方程的扩散极限。在有界凸多边形上，我们从内部调和场、平坦边层和动力学楔层组装了一个复合近似，并证明该解在$L^{\boldsymbol{\infty}}$中以显式代数速率收敛到该复合近似，且在内部的紧子集上一致收敛到调和场本身。我们还给出了动力学楔层的完整公式适定性理论，包括其代数衰减特性。证明结合了特征稳定性估计、加权Mellin映射定理、双层构造与匹配方案，以及楔校正子的移位超调和障碍。作为次要结果，我们证明在任意有界简单多边形（包括具有凹顶点的多边形）上，$L^{2}$中以平方根速率收敛。该论证仅需端点截断的边层和双检验抵消，完全不需要动力学楔层。
英文摘要
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.
Comments90 pages; adjust parameters ranges to strengthen the results
