{"title":"晶体运动对多边形弯曲锋面的运动:v形解和最终单调性","authors":"T. Ishiwata","doi":"10.3934/proc.2011.2011.717","DOIUrl":null,"url":null,"abstract":"This paper deals with behavior of polygonal plane curves with two \nasymptotic lines by generalized crystalline curvature flow with a driving force. \nWe show global existence of V-shaped solutions and investigate the deformation \npatterns of non-V-shaped solutions. We also show that non-V-shaped solutions \nbecome V-shaped in finite time.","PeriodicalId":210679,"journal":{"name":"Default journal","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Motion of polygonal curved fronts by crystalline motion: V-shaped solutions and eventual monotonicity\",\"authors\":\"T. Ishiwata\",\"doi\":\"10.3934/proc.2011.2011.717\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with behavior of polygonal plane curves with two \\nasymptotic lines by generalized crystalline curvature flow with a driving force. \\nWe show global existence of V-shaped solutions and investigate the deformation \\npatterns of non-V-shaped solutions. We also show that non-V-shaped solutions \\nbecome V-shaped in finite time.\",\"PeriodicalId\":210679,\"journal\":{\"name\":\"Default journal\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Default journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/proc.2011.2011.717\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Default journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/proc.2011.2011.717","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Motion of polygonal curved fronts by crystalline motion: V-shaped solutions and eventual monotonicity
This paper deals with behavior of polygonal plane curves with two
asymptotic lines by generalized crystalline curvature flow with a driving force.
We show global existence of V-shaped solutions and investigate the deformation
patterns of non-V-shaped solutions. We also show that non-V-shaped solutions
become V-shaped in finite time.
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