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Title: Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature (English)
Author: Yazaki, Shigetoshi
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 6
Year: 2007
Pages: 903-912
Summary lang: English
Category: math
Summary: Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity. (English)
Keyword: essentially admissible polygon
Keyword: crystalline curvature
Keyword: the Wulff shape
Keyword: isoperimetric inequality
MSC: 34A26
MSC: 34A34
MSC: 34K25
MSC: 39A12
MSC: 53A04
MSC: 74N05
MSC: 82D25
idZBL: Zbl 1139.53032
idMR: MR2388403
Date available: 2009-09-24T20:31:04Z
Last updated: 2013-09-21
Stable URL:
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