Mullins-Sekerka问题中平面界面的松弛

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2017-09-14 DOI:10.4171/IFB/415

Olga Chugreeva, F. Otto, Maria G. Westdickenberg

{"title":"Mullins-Sekerka问题中平面界面的松弛","authors":"Olga Chugreeva, F. Otto, Maria G. Westdickenberg","doi":"10.4171/IFB/415","DOIUrl":null,"url":null,"abstract":"We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in the context of the 1-d Cahn-Hilliard equation and the current work represents an extension to a higher dimensional problem in which the curvature of the interface plays an important role. The convergence rates obtained are optimal given the assumptions on the initial data.","PeriodicalId":13863,"journal":{"name":"Interfaces and Free Boundaries","volume":"76 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2017-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Relaxation to a planar interface in the Mullins–Sekerka problem\",\"authors\":\"Olga Chugreeva, F. Otto, Maria G. Westdickenberg\",\"doi\":\"10.4171/IFB/415\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in the context of the 1-d Cahn-Hilliard equation and the current work represents an extension to a higher dimensional problem in which the curvature of the interface plays an important role. The convergence rates obtained are optimal given the assumptions on the initial data.\",\"PeriodicalId\":13863,\"journal\":{\"name\":\"Interfaces and Free Boundaries\",\"volume\":\"76 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2017-09-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Interfaces and Free Boundaries\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/IFB/415\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Interfaces and Free Boundaries","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/IFB/415","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

应用基于距离、能量和耗散关系的松弛方法，分析了Mullins-Sekerka模型中到平面界面的收敛速率。松弛方法是由两位作者在一维Cahn-Hilliard方程的背景下开发的，目前的工作代表了对高维问题的扩展，其中界面曲率起着重要作用。在给定初始数据的前提下，得到的收敛率是最优的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Relaxation to a planar interface in the Mullins–Sekerka problem

We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in the context of the 1-d Cahn-Hilliard equation and the current work represents an extension to a higher dimensional problem in which the curvature of the interface plays an important role. The convergence rates obtained are optimal given the assumptions on the initial data.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.