On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect

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Abstract

The behavior of polygonal curves with asymptotic lines to crys- talline motion with the bulk e ect is discussed. We show sufficient conditions for global existence of the solutions and characterize facet-extinction patterns. We also show the eventual monotonicity of shape of the solution curves, that is, the solutions become V-shaped in finite time.

Original languageEnglish
Pages (from-to)865-873
Number of pages9
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume4
Issue number4
DOIs
Publication statusPublished - 2011 Aug

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Crystalline materials

Keywords

  • Crystalline curvature
  • Crystalline motion
  • Eventual monotonicity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

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title = "On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect",
abstract = "The behavior of polygonal curves with asymptotic lines to crys- talline motion with the bulk e ect is discussed. We show sufficient conditions for global existence of the solutions and characterize facet-extinction patterns. We also show the eventual monotonicity of shape of the solution curves, that is, the solutions become V-shaped in finite time.",
keywords = "Crystalline curvature, Crystalline motion, Eventual monotonicity",
author = "Tetsuya Ishiwata",
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AB - The behavior of polygonal curves with asymptotic lines to crys- talline motion with the bulk e ect is discussed. We show sufficient conditions for global existence of the solutions and characterize facet-extinction patterns. We also show the eventual monotonicity of shape of the solution curves, that is, the solutions become V-shaped in finite time.

KW - Crystalline curvature

KW - Crystalline motion

KW - Eventual monotonicity

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