| Issue |
ESAIM: M2AN
Volume 33, Number 4, July August 1999
|
|
|---|---|---|
| Page(s) | 797 - 806 | |
| DOI | https://doi.org/10.1051/m2an:1999164 | |
| Published online | 15 August 2002 | |
Motion of spirals by crystalline curvature
1
Department of Applied Physics and
Mathematics, Faculty of Engineering, University of Tokushima, Tokushima
770-8506, Japan. imai@pm.tokushima-v.ac.jp.
2
Department of Mathematics, Hitotsubashi
University, Kunitachi, Tokyo 186-8601, Japan.
3
Graduate School of Mathematical Sciences,
University of Tokyo, Komaba, Tokyo 153-8914, Japan.
Received:
2
March
1998
Revised:
2
October
1998
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.
Mathematics Subject Classification: 80A22 / 34A12 / 52C99
Key words: Crystalline motion / spiral-shaped polygonal curves / material sciences.
© EDP Sciences, SMAI, 1999
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