本文在${\rm I \! R}^3$中研究了作用在圆柱$\mathcal{C}_r$的一类一般（非轴对称）扰动上的表面扩散流。使用工具，从抛物理论的一致定期流形，最大的正则性，我们建立的表面扩散流的解决方案的存在性和唯一性从（空间-无界）表面定义在$\mathcal{C}_r$通过标量高度函数是一致有界的中心圆柱轴。此外，我们表明，$\mathcal{C}_r$通常是稳定的$2 π$ -轴向-周期扰动，如果半径$r > 1$，和不稳定的，如果$0 < r < 1$。稳定性也被证明持有轴向诺依曼边界条件的设置。
英文摘要：
We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders $\mathcal{C}_r$ in ${\rm I \! R}^3$. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially--unbounded) surfaces defined over $\mathcal{C}_r$ via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that $\mathcal{C}_r$ is normally stable with respect to $2 π$--axially--periodic perturbations if the radius $r > 1$,and unstable if $0 < r < 1$. Stability is also shown to hold in settings with axial Neumann boundary conditions.
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