修正的退化卡恩-希利亚德表面扩散模型的弱解

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Xiaohua Niu, Yang Xiang, Xiaodong Yan
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引用次数: 0

摘要

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。
Weak solutions for a modified degenerate Cahn–Hilliard model for surface diffusion
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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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
59
审稿时长
6 months
期刊介绍: Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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