发表机构
Mathematics and Science College, Shanghai Normal University（上海师范大学数理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究Robin边界条件下平面带状区域中受迫曲率流的渐近行为，发现高度、速度和梯度发散，而归一化斜率与速度分别收敛于1和强迫参数，曲率测度集中于对称轴。
AI 中文摘要
我们研究在平面带状区域中，受Robin边界条件约束的图形受迫平均曲率流。法向速度由 $V=H+b$ 给出，其中 $b>0$ 为常数，$H$ 表示图形的曲率。我们考虑正偶解，并将问题化简到半区间上。主要结果描述了由Robin条件产生的退化现象：高度、瞬时速度和空间梯度发散，而归一化斜率 $u_x/u$ 在远离对称轴处收敛于1。归一化速度 $u_t/u$ 收敛于强迫参数 $b$。曲率在内部以积分意义收敛到零，而其水平曲率测度集中于对称轴。
英文摘要
We study the graphical forced mean curvature flow in a planar strip subject to Robin boundary conditions. The normal velocity is prescribed by $V=H+b$, where $b>0$ is constant and $H$ denotes the curvature of the graph. We consider positive even solutions and reduce the problem to the half interval. The main results describe the degeneration produced by the Robin condition: the height, the instantaneous velocity, and the spatial gradient diverge, while the normalized slope $u_x/u$ converges to one away from the symmetry axis. The normalized velocity $u_t/u$ converges to the forcing parameter $b$. The curvature converges to zero in the interior in an integral sense, whereas its horizontal curvature measure concentrates at the symmetry axis.
Comments15 pages
