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Title: Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion (English)
Author: Ishiwata, Tetsuya
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 140
Issue: 2
Year: 2015
Pages: 111-119
Summary lang: English
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Category: math
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Summary: We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never occurs. Finally, we show that spiral-shaped solutions exist globally in time. (English)
Keyword: curvature driven motion
Keyword: crystalline curvature
Keyword: spiral growth
MSC: 34A26
MSC: 34A34
MSC: 39A12
MSC: 74N05
MSC: 82D25
idZBL: Zbl 06486927
idMR: MR3368487
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Date available: 2015-06-30T12:09:37Z
Last updated: 2016-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/144318
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Reference: [1] Gurtin, M. E.: Thermomechanics of Evolving Phase Boundaries in the Plane.Oxford Mathematical Monographs Clarendon Press, Oxford (1993). Zbl 0787.73004, MR 1402243
Reference: [2] Ishiwata, T.: Motion of non-convex polygons by crystalline curvature and almost convexity phenomena.Japan J. Ind. Appl. Math. 25 (2008), 233-253. Zbl 1155.53033, MR 2431681, 10.1007/BF03167521
Reference: [3] Ishiwata, T.: Crystalline motion of spiral-shaped polygonal curves with a tip motion.Discrete Contin. Dyn. Syst., Ser. S 7 (2014), 53-62. Zbl 1273.82076, MR 3082855, 10.3934/dcdss.2014.7.53
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