Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-28 DOI:10.57262/ade027-1112-823

Andrew Colinet

引用次数: 2

Abstract

In the setting of a compact Riemannian manifold of dimension N ≥ 3 we provide a structural description of the limiting behaviour of the energy measures of solutions to the parabolic Ginzburg-Landau equation. In particular, we provide a decomposition of the limiting energy measure into a diffuse part, which is absolutely continuous with respect to the volume measure, and a concentrated part supported on a codimension 2 rectifiable subset. We also demonstrate that the time evolution of the diffuse part is determined by the heat equation while the concentrated part evolves according to a Brakke flow. This paper extends the work of Bethuel, Orlandi, and Smets from [8].

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闭流形上抛物型Ginzburg-Landau方程极限的结构描述

在维数N≥3的紧致黎曼流形上，我们给出了抛物型Ginzburg-Landau方程解的能量测度的极限性质的结构描述。特别地，我们将极限能量测度分解为相对于体积测度绝对连续的扩散部分和支持在余维2可直子集上的集中部分。我们还证明了扩散部分的时间演化是由热方程决定的，而集中部分是根据Brakke流演化的。本文扩展了Bethuel、Orlandi和Smets在[8]中的工作。

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

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