关于抛物型Allen-Cahn方程的熵

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2018-12-20 DOI:10.4171/ifb/460

Ao Sun

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引用次数: 1

摘要

本文定义了Radon测度的熵，特别是与抛物型Allen-Cahn方程相关的测度。我们表明，当初始数据的熵足够小(小于一维驻波能量的两倍)时，抛物型Allen-Cahn方程的极限测度具有单位密度。

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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On the entropy of parabolic Allen–Cahn equation

In this paper we define the entropy of Radon measures, especially the measures associated to the parabolic Allen-Cahn equation. We show that when the entropy of the initial data is small enough (less than twice of the energy of the one dimensional standing wave), the limit measure of the parabolic Allen-Cahn equation has unit density.

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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.