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

Tetsuya Ishiwata

doi:10.3934/dcdss.2011.4.865

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

Tetsuya Ishiwata

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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 language	English
Pages (from-to)	865-873
Number of pages	9
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	4
Issue number	4
DOIs	https://doi.org/10.3934/dcdss.2011.4.865
Publication status	Published - 2011 Aug

Keywords

Crystalline curvature
Crystalline motion
Eventual monotonicity

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdss.2011.4.865

Cite this

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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.",

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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.

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KW - Eventual monotonicity

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

Abstract

Keywords

ASJC Scopus subject areas

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