Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/mine.2023090

Ko-Shin Chen, C. Muratov, Xiaodong Yan

引用次数: 0

Abstract

We study layered solutions in a one-dimensional version of the scalar Ginzburg-Landau equation that involves a mixture of a second spatial derivative and a fractional half-derivative, together with a periodically modulated nonlinearity. This equation appears as the Euler-Lagrange equation of a suitably renormalized fractional Ginzburg-Landau energy with a double-well potential that is multiplied by a 1-periodically varying nonnegative factor $ g(x) $ with $ \int_0^1 \frac{1}{g(x)} dx < \infty. $ A priori this energy is not bounded below due to the presence of a nonlocal term in the energy. Nevertheless, through a careful analysis of a minimizing sequence we prove existence of global energy minimizers that connect the two wells at infinity. These minimizers are shown to be the classical solutions of the associated nonlocal Ginzburg-Landau type equation.

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具有周期调制的非局部金兹堡-朗道模型的分层解

我们研究了一维版本的标量金兹堡-朗道方程的分层解，该方程涉及二阶空间导数和分数半导数的混合，以及周期调制非线性。这个方程表现为一个适当的重归一化分数金兹堡-朗道能量的欧拉-拉格朗日方程，它具有双阱势，乘以1周期变化的非负因子$ g(x) $与$ \int_0^1 \frac{1}{g(x)} dx < \infty. $先验地，由于能量中存在非局域项，该能量不受限制。然而，通过对最小化序列的仔细分析，我们证明了在无穷远处连接两个井的全局能量最小化的存在。这些最小值被证明是相关的非局部金兹堡-朗道型方程的经典解。

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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.