On spiral solutions to generalized crystalline motion with a rotating tip motion

研究成果: Article

抄録

In our previous paper we proposed a crystalline motion of spiral- shaped polygonal curves with a tip motion as a simple model of a step motion on a crystal surface under screw dislocation and discussed global existence of spiral solutions to the proposed model. In this paper we extend the previous results for generalized crystalline curvature ow with a suitable tip motion. We show that solution curves never intersect a trajectory of a tip and has no self-intersections. We also show that any facet never disappear during time evolution. Finally we show a time-global existence of the spiral-shaped solu- tions.

元の言語English
ページ(範囲)881-888
ページ数8
ジャーナルDiscrete and Continuous Dynamical Systems - Series S
8
発行部数5
DOI
出版物ステータスPublished - 2015 10 1

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Crystalline materials
Screw dislocations
Trajectories
Crystals

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

これを引用

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abstract = "In our previous paper we proposed a crystalline motion of spiral- shaped polygonal curves with a tip motion as a simple model of a step motion on a crystal surface under screw dislocation and discussed global existence of spiral solutions to the proposed model. In this paper we extend the previous results for generalized crystalline curvature ow with a suitable tip motion. We show that solution curves never intersect a trajectory of a tip and has no self-intersections. We also show that any facet never disappear during time evolution. Finally we show a time-global existence of the spiral-shaped solu- tions.",
keywords = "Crystalline curvature, Motion by curvature, Polygonal curves, Spirals",
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AB - In our previous paper we proposed a crystalline motion of spiral- shaped polygonal curves with a tip motion as a simple model of a step motion on a crystal surface under screw dislocation and discussed global existence of spiral solutions to the proposed model. In this paper we extend the previous results for generalized crystalline curvature ow with a suitable tip motion. We show that solution curves never intersect a trajectory of a tip and has no self-intersections. We also show that any facet never disappear during time evolution. Finally we show a time-global existence of the spiral-shaped solu- tions.

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