封闭平面曲线上的熵梯度流

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-07-27 DOI:10.1007/s00205-024-02014-7

Lachlann O’Donnell, Glen Wheeler, Valentina-Mira Wheeler

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引用次数: 0

摘要

在本文中，我们考虑了熵函数的陡降（L^2）梯度流。该流扩展凸曲线，初始圆的半径像时间的平方根一样增长。我们的主要结果是，对于任何初始曲线（无论是浸入类 \(C^2\)的局部严格凸曲线还是嵌入类 \(W^{2,2}\)的以严格凸体为边界的曲线），熵流都会平滑地收敛到一个不断扩张的多重覆盖圆。

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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The Gradient Flow for Entropy on Closed Planar Curves

In this paper we consider the steepest descent \(L^2\)-gradient flow of the entropy functional. The flow expands convex curves, with the radius of an initial circle growing like the square root of time. Our main result is that, for any initial curve (either immersed locally strictly convex of class \(C^2\) or embedded of class \(W^{2,2}\) bounding a strictly convex body), the flow converges smoothly to a round expanding multiply-covered circle.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.