Crystalline motion of spiral-shaped polygonal curves with a tip motion

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4 Citations (Scopus)

Abstract

In this paper we propose 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. We give a tip motion and discuss the behavior of the solution curves by crystalline curvature flow with a driving force. We show that the solution curve belongs to a suitable class of spiral- shaped curves and also show a time-global existence of the spiral-shaped solutions.

Original languageEnglish
Pages (from-to)53-62
Number of pages10
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume7
Issue number1
DOIs
Publication statusPublished - 2014 Feb 1

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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