Motion of spirals by crystalline curvature
Department of Applied Physics and
Mathematics, Faculty of Engineering, University of Tokushima, Tokushima
770-8506, Japan. email@example.com.
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.
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