{"title":"Well-Posedness of a Pseudo-Parabolic KWC System in Materials Science","authors":"Harbir Antil, Daiki Mizuno, Ken Shirakawa","doi":"10.1137/24m163952x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6422-6445, October 2024. <br/> 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.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/24m163952x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
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