关于一个四元非局部等周问题

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
S. Alama, L. Bronsard, Xinyang Lu, Chong Wang
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引用次数: 1

摘要

我们研究了一个二维的四元抑制系统。这种自由能函数将有利于微畴生长的界面能与防止微畴无限扩展的库仑型长程相互作用能相结合。在这里,我们考虑一个极限,其中三个物种非常小,但相互作用相应地很大,以保持一个非平凡的极限。在这个极限中,区分了两个能级:最高阶极限将局部结构的几何信息编码为三分量等周问题,而第二个能级描述全局极小值中分量的空间分布。导出了极限配置的几何描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On a quaternary nonlocal isoperimetric problem
We study a two-dimensional quaternary inhibitory system. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited spreading. Here we consider a limit in which three species are vanishingly small, but interactions are correspondingly large to maintain a nontrivial limit. In this limit two energy levels are distinguished: the highest order limit encodes information on the geometry of local structures as a three-component isoperimetric problem, while the second level describes the spatial distribution of components in global minimizers. Geometrical descriptions of limit configurations are derived.
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来源期刊
Quarterly of Applied Mathematics
Quarterly of Applied Mathematics 数学-应用数学
CiteScore
1.90
自引率
12.50%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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