标题： 具有高维双井势的罗宾边界条件下向量值Allen-Cahn方程 显示英文标题

标题： The vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions

摘要： 本文研究了带有多维双井势的向量值Allen-Cahn方程在Robin边界条件下的问题。 我们证明了对于一大类边界能量密度和准备充分的初始数据，解在局部时间范围内收敛到具有固定接触角$0<\alpha\leq 90^\circ$的平均曲率流。 推导出极限的清晰界面系统，其中包括主体中的调和热流以及相界处的最小配对条件。 分析结合了相对熵方法、梯度流校准和弱收敛技术。 这些结果推广了之前关于无边界效应的向量值情形（《纯应用数学通讯》，78:1199-1247, 2025）以及具有边界接触能的标量值情形（《变分偏微分方程杂志》，61:201, 2022）的研究工作。 显示英文摘要

摘要： This work investigates the vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions. We establish local-in-time convergence of solutions to mean curvature flow with a fixed contact angle $0<\alpha\leq 90^\circ$, for a broad class of boundary energy densities and well-prepared initial data. The limiting sharp-interface system is derived, comprising harmonic heat flows in the bulk and minimal pair conditions at phase boundaries. The analysis combines the relative entropy method with gradient flow calibrations and weak convergence techniques. These results extend prior works on the analysis of the vector-valued case without boundary effects (Comm. Pure Appl. Math., 78:1199-1247, 2025) and the scalar-valued case with boundary contact energy (Calc. Var. Partial Differ. Equ., 61:201, 2022).