{"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}
引用次数: 6
Abstract
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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