晶粒边界运动相场模型初始边界值问题的全局解决方案

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI:10.1137/22m1477775

Xingzhi Bian, Peicheng Zhu, Boling Guo, Ying Zhang

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4296-4323 页，2024 年 8 月。摘要我们将证明一个椭圆-抛物耦合系统的新型相场模型的初始边界值问题的弱解的全局存在性。提出该模型的目的是试图描述晶粒边界的运动，这是一种由弹性变形固体中的体自由能驱动的界面扩散运动。其应用包括材料科学中出现的重要过程，如烧结。在该模型中，阶次参数的演化方程是一个非均匀、退化的四阶抛物线方程，它与卡恩-希利亚德方程的区别在于未知数梯度的非光滑项。

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Global Solutions to an Initial-Boundary Value Problem of a Phase-Field Model for Motion of Grain Boundaries

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4296-4323, August 2024.
Abstract. We shall prove the global existence of weak solutions to an initial boundary value problem for a novel phase-field model which is an elliptic-parabolic coupled system. This model is proposed as an attempt to describe the motion of grain boundaries, a type of interface motion by interface diffusion driven by bulk free energy in elastically deformable solids. Its applications include important processes arising in materials science, e.g., sintering. In this model the evolution equation for an order parameter is a nonuniformly, degenerate parabolic equation of fourth order, which differs from the Cahn–Hilliard equation by a nonsmooth term of the gradient of the unknown.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.