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Motion of spirals by crystalline curvature

Published online by Cambridge University Press:  15 August 2002

Hitoshi Imai ,
Naoyuki Ishimura  and
TaKeo Ushijima
Hitoshi Imai
Affiliation:
Department of Applied Physics and Mathematics, Faculty of Engineering, University of Tokushima, Tokushima 770-8506, Japan. imai@pm.tokushima-v.ac.jp.
Naoyuki Ishimura
Affiliation:
Department of Mathematics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan.
TaKeo Ushijima
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914, Japan.
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Abstract

Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.

Keywords

Crystalline motionspiral-shaped polygonal curvesmaterial sciences.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 4 , July 1999 , pp. 797 - 806
Copyright
© EDP Sciences, SMAI, 1999

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