Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature
Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature
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作者：
S. Yazaki
研究了一类保面积晶体曲率流方程解的渐近行为。在这个方程中，被溶液多边形包围的面积保持不变，而它的总界面结晶能保持下降。在初始多边形本质上是可容许的和凸的情况下，如果最大存在时间是有限的，则消失边本质上是可容许边。这与初始多边形是可接受的和凸的情况形成对比：随着时间趋于无穷，解决多边形会收敛到WUL形状的边界，而没有消失的边。
Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wul shape without vanishing edges as time tends to infinity.