Bifurcations of spherically asymmetric solutions to an evolution equation for curves

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-26 DOI:10.4171/ifb/474

Takeo Sugai

引用次数: 0

Abstract

We show that a certain non-local curvature flow for planar curves has non-trivial self-similar solutions with $n$-fold rotational symmetry, bifurcated from a trivial circular solution. Moreover, we show that the trivial solution is stable with respect to perturbations which keep the geometric center and the enclosed area, and that, for $n$ different from 3, the $n$-fold symmetric solution is stable with respect to perturbations which satisfy the same conditions as above and have the same symmetry as the solutions.

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一类曲线演化方程球不对称解的分岔

我们证明了一类平面曲线的非局部曲率流具有$n$-折旋转对称的非平凡自相似解，它是由一个平凡圆解分叉而来的。此外，我们证明了平凡解对于保持几何中心和封闭区域的扰动是稳定的，并且，对于n$不同于3的扰动，n$折叠对称解对于满足上述相同条件且与解具有相同对称性的扰动是稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.