On a length-preserving inverse curvature flow of convex closed plane curves

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Gao, Laiyuan¹  Pan, Shengliang²  Tsai, Dong-Ho³ 

[1] Jiangsu Normal Univ, Sch Math & Stat, 101 Shanghai Rd, Xuzhou 221116, Jiangsu, Peoples R China

[2] Tongji Univ, Sch Math Sci, 1239 Siping Rd, Shanghai 200092, Peoples R China

[3] Natl Tsing Hua Univ, Dept Math, 101,Sect 2,Kuang Fu Rd, Hsinchu 30013, Taiwan

关键词: Convex curve;    Inverse curvature flow;    Length-preserving;    Nonlocal flow;   

DOI  :  10.1016/j.jde.2020.04.028

来源: Elsevier

【 摘 要 】

This paper deals with a 1/kappa(alpha)-type length-preserving nonlocal flow of convex closed plane curves for all alpha > 0. Under this flow, the convexity of the evolving curve is preserved. For a global flow, it is shown that the evolving curve converges smoothly to a circle as t -> infinity. Some numerical blow-up examples and a sufficient condition leading to the global existence of the flow are also constructed. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free