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

Tetsuya Ishiwata

doi:10.3934/dcdss.2011.4.865

Article Contents

2011, Volume 4, Issue 4: 865-873. Doi: 10.3934/dcdss.2011.4.865

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

Tetsuya Ishiwata^1,

1.
Shibaura Institute of Technology, Fukasaku 309, Minuma-ku, Saitama, 337-8570

Received: August 31, 2009

Revised: October 31, 2009

Published: July 2011

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Abstract

The behavior of polygonal curves with asymptotic lines to crystalline motion with the bulk effect 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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Mathematics Subject Classification: Primary: 34A34, 39A12, 74N05; Secondary: 53A04, 34A26.

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References

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