{"title":"Microstructural evolution in 3D: An existence result","authors":"David Kinderlehrer , KiHyun Yun","doi":"10.1016/j.na.2025.113810","DOIUrl":null,"url":null,"abstract":"<div><div>Microstructural coarsening is a network of grains separated by interfaces, facets, that evolve by generalized curvature. The facets meet along curves that come together at points. Systems of this nature consist of many nonlinear PDEs with their boundary conditions. Here we explore the local in time existence for a configuration, perhaps the simplest, close to a known equilibrium configuration.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113810"},"PeriodicalIF":1.3000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X25000641","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Microstructural coarsening is a network of grains separated by interfaces, facets, that evolve by generalized curvature. The facets meet along curves that come together at points. Systems of this nature consist of many nonlinear PDEs with their boundary conditions. Here we explore the local in time existence for a configuration, perhaps the simplest, close to a known equilibrium configuration.
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Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.
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