Well-Posedness of a Pseudo-Parabolic KWC System in Materials Science

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-09-17 DOI:10.1137/24m163952x

Harbir Antil, Daiki Mizuno, Ken Shirakawa

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6422-6445, October 2024.
Abstract. The original KWC system is widely used in materials science. It was proposed in [R. Kobayashi, J. A. Warren, and W. C. Carter, Phys. D, 140 (2000), pp. 141–150] and is based on the phase field model of planar grain boundary motion. This model suffers from two key challenges. First, it is difficult to establish its relation to physics, in particular a variational model. Second, it lacks uniqueness. The former has been recently studied within the realm of BV theory. The latter only holds under various simplifications. This article introduces a pseudo-parabolic version of the KWC system. A direct relationship with variational model (as gradient flow) and uniqueness are established without making any unrealistic simplifications. Namely, this is the first KWC system which is both physically and mathematically valid. The proposed model overcomes the well-known open issues.

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材料科学中伪抛物 KWC 系统的良好拟合

SIAM 数学分析期刊》，第 56 卷第 5 期，第 6422-6445 页，2024 年 10 月。摘要。原始 KWC 系统广泛应用于材料科学领域。它是在[R.Kobayashi, J. A. Warren, and W. C. Carter, Phys. D, 140 (2000), pp.该模型面临两大挑战。首先，很难确定它与物理学的关系，特别是与变分模型的关系。其次，它缺乏唯一性。前者最近已在 BV 理论范畴内得到研究。后者只有在各种简化条件下才成立。本文介绍了 KWC 系统的伪抛物线版本。在不做任何不切实际的简化的情况下，建立了与变分模型（如梯度流）和唯一性的直接关系。也就是说，这是第一个在物理和数学上都有效的 KWC 系统。所提出的模型克服了众所周知的未决问题。

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

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.