摘要
研究了一类含参数的非局部平面凸曲线流,应用偏微分方程的极大值原理和先验估计,证明了发展曲线在演化过程中保持凸性,曲线的周长和面积均单调递减,曲线越变越圆且在有限时间内收缩于一点.
In this paper,a kind of nonlocal plane convex curve flow has been discussed.From the maximum principle and a priori estimates of partial differential equations,it is proved that the convex curve preserves convexity,the perimeter of the evolving curve and the area it bounds decrease monotonically,and the convex curve becomes more and more circular and shrinks to a point in finite time.
出处
《西南师范大学学报（自然科学版）》
CAS
北大核心
2017年第12期12-17,共6页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(41671409)
河南省科技攻关项目(172012201553)
关键词
偏微分方程
曲线收缩流
凸曲线
partial differential equation
curve shortening flow
convex curves
