{"title":"晶粒边界运动相场模型初始边界值问题的全局解决方案","authors":"Xingzhi Bian, Peicheng Zhu, Boling Guo, Ying Zhang","doi":"10.1137/22m1477775","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4296-4323, August 2024. <br/> 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.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global Solutions to an Initial-Boundary Value Problem of a Phase-Field Model for Motion of Grain Boundaries\",\"authors\":\"Xingzhi Bian, Peicheng Zhu, Boling Guo, Ying Zhang\",\"doi\":\"10.1137/22m1477775\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4296-4323, August 2024. <br/> 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.\",\"PeriodicalId\":51150,\"journal\":{\"name\":\"SIAM Journal on Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-07-01\",\"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/10.1137/22m1477775\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1477775","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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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