| 摘要: |
| 本文证明了一类保长度流下, 初始为欧氏平面星形中心对称闭曲线的演化过程具有渐近收敛性: 在任意阶可微的意义下, 这些曲线最终都会光滑地变形为一个标准圆. |
| 关键词: 保长度流 星形曲线 发散型拟线性抛物方程 |
| DOI： |
| 分类号:O186.11 |
| 基金项目:国家自然科学基金项目 (12261105) |
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| A planar star-shaped closed curve evolving under a class of length-preserving flow |
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Cheng Qiyuan, Guo Shunzi
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Department of Mathematics, Yunnan Normal University, Kunming 650500, PR China
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| Abstract: |
| This paper proves that under a class of length-preserving flows, the evolution process of closed curves which are initially star-shaped, centrally symmetric, and lie in the Euclidean plane possesses asymptotic convergence: in the sense of being differentiable of any order, these curves will eventually deform smoothly into a standard circle. |
| Key words: Length-preserving flow Star-shaped curve Divergret quasi-linear parabolic equation |
