平面中一类曲线流的收敛率  

Convergence Rate of a Curve Flow in a Plane

作　　者：孙乔乔 SUN Qiaoqiao(College of Mathematics and Physics,Wenzhou University,Wenzhou,China 325035)

机构地区：[1]温州大学数理学院,浙江温州325035

出　　处：《温州大学学报(自然科学版)》2025年第1期10-16,共7页Journal of Wenzhou University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971355)。

摘　　要：研究了平面中的一簇单参数曲线流,推广了Tsai等引入的两种曲线流.当初始曲线是平面闭合凸曲线时,对任意的t∈[0,+∞),曲线流的解都存在且保持凸性,曲线的长度单调减,曲线所围图形的面积单调增.特别地,证明了曲线到圆的收敛速率:当t→+∞时,等周比L^(2)-4πA以指数函数的速度收敛于0,与此同时曲线的内半径和外半径之比以指数函数的速度收敛于1.This paper studies a cluster of single-parameter curve flows in the plane and interpolates two types of curve flows studied by Tsai etc.When the initial curve is an in-plane closed convex curve,then for any t∈[0,+∞),the solution of the curve flow exists and the curve remains convex.The length of the curve decreases monotonically,and the area of the closed graph enclosed by the curve increases monotonically.In particular,the convergence rate of the curve to a circle is proven:when t→+∞,the equiweekly ratio L^(2)-4πA converges at the speed of the exponential function to 0,while the ratio of the inner and outer radii of the curve converges at the speed of the exponential function to 1.

关 键 词：凸曲线 极大值原理 曲线收缩流 

分 类 号：O186.1[理学—数学]