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

Tetsuya Ishiwata

doi:10.3934/dcdss.2014.7.53

Article Contents

2014, Volume 7, Issue 1: 53-62. Doi: 10.3934/dcdss.2014.7.53

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

Tetsuya Ishiwata^1,

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

Received: March 2012

Revised: August 2012

Published online: July 2013

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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.

Keywords:

Mathematics Subject Classification: 34A34, 39A12, 74N05, 74N20, 53A04.

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References

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