Weak solutions for a modified degenerate Cahn–Hilliard model for surface diffusion

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-01 DOI:10.4310/cms.2024.v22.n2.a8

Xiaohua Niu, Yang Xiang, Xiaodong Yan

引用次数: 0

Abstract

In this paper, we study the weak solutions of a modified degenerate Cahn–Hilliard type model for surface diffusion. With degenerate phase-dependent diffusion mobility and additional stabilizing function, this model is able to give the correct sharp interface limit. We introduce a notion of weak solutions for the nonlinear model. The existence of such solutions is obtained by approximations of the proposed model with non-degenerate mobilities. We also employ this method to prove the existence of weak solutions to a related model where the chemical potential contains a nonlocal term originating from self-climb of dislocations in crystalline materials.

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修正的退化卡恩-希利亚德表面扩散模型的弱解

在本文中，我们研究了修正的退化卡恩-希利亚德表面扩散模型的弱解。通过退化的相依赖扩散流动性和额外的稳定函数，该模型能够给出正确的尖锐界面极限。我们为非线性模型引入了弱解的概念。通过对所提出模型的非退化迁移率进行近似，可以得到这种解的存在性。我们还利用这种方法证明了一个相关模型的弱解的存在，在这个模型中，化学势包含一个源自晶体材料中位错自爬行的非局部项。

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.