Mathematical analysis for interface dynamics of crystal

在本研究中，我们考虑了一些晶体运动：一种晶体的界面运动。特别是，我们主要处理两种类型的晶体运动：具有体积效应的晶体曲率流动和保持面积的晶体曲率流动。我们讨论了解曲线的行为，而不是渐近行为，完整地分类了界面线段的消光模式，得到了界面无自交条件下解曲线的变形过程。

In this research, we consider some crystalline motions : a kind of interface motion of crystal. In particular, we mainly treat 2 types of crystalline motion : crystalline curvature flow with bulk effect and area-preserving crystalline curvature flow. We discuss the behavior of solution curves, not asymptotic behavior, and classify the extinction patterns of a line-segment of the interface completely and obtain the deformation process of solution curve under the conditions for no self-intersection of the interface.