Uniqueness of the blow-down limit for a triple junction problem

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2024-10-09 DOI:10.1002/cpa.22230

Zhiyuan Geng

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引用次数: 0

Abstract

We prove the uniqueness of $L^{1}$ blow-down limit at infinity for an entire minimizing solution $u : R^{2} \to R^{2}$ of a planar Allen–Cahn system with a triple-well potential. Consequently, $u$ can be approximated by a triple junction map at infinity. The proof exploits a careful analysis of energy upper and lower bounds, ensuring that the diffuse interface remains within a small neighborhood of the approximated triple junction at all scales.

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三重结点问题的炸毁极限唯一性

我们证明了具有三孔势能的平面 Allen-Cahn 系统的整个最小解在无穷远处的炸毁极限的唯一性。因此，在无穷远处可以用三重结点图来近似。证明利用了对能量上界和下界的仔细分析，确保扩散界面在所有尺度上都保持在近似三重交界处的小邻域内。

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

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.