{"title":"给定接触角的曲线域平均曲率流的最小运动格式及其计算","authors":"Tokuhiro Eto, Yoshikazu Giga","doi":"10.1007/s10231-023-01398-9","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce a capillary Chambolle-type scheme for mean curvature flow with prescribed contact angle. Our scheme includes a capillary functional instead of just the total variation. We show that the scheme is well-defined and has consistency with the energy minimizing scheme of Almgren–Taylor–Wang type. Moreover, for a planar motion in a strip, we give several examples of numerical computation of this scheme based on the split Bregman method instead of a duality method.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01398-9.pdf","citationCount":"0","resultStr":"{\"title\":\"On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation\",\"authors\":\"Tokuhiro Eto, Yoshikazu Giga\",\"doi\":\"10.1007/s10231-023-01398-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce a capillary Chambolle-type scheme for mean curvature flow with prescribed contact angle. Our scheme includes a capillary functional instead of just the total variation. We show that the scheme is well-defined and has consistency with the energy minimizing scheme of Almgren–Taylor–Wang type. Moreover, for a planar motion in a strip, we give several examples of numerical computation of this scheme based on the split Bregman method instead of a duality method.</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-11-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10231-023-01398-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10231-023-01398-9\",\"RegionNum\":3,\"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":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-023-01398-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation
We introduce a capillary Chambolle-type scheme for mean curvature flow with prescribed contact angle. Our scheme includes a capillary functional instead of just the total variation. We show that the scheme is well-defined and has consistency with the energy minimizing scheme of Almgren–Taylor–Wang type. Moreover, for a planar motion in a strip, we give several examples of numerical computation of this scheme based on the split Bregman method instead of a duality method.
期刊介绍:
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.