In our previous paper we proposed 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 and discussed global existence of spiral solutions to the proposed model. In this paper we extend the previous results for generalized crystalline curvature ow with a suitable tip motion. We show that solution curves never intersect a trajectory of a tip and has no self-intersections. We also show that any facet never disappear during time evolution. Finally we show a time-global existence of the spiral-shaped solu- tions.
|ジャーナル||Discrete and Continuous Dynamical Systems - Series S|
|出版物ステータス||Published - 2015 10 1|
ASJC Scopus subject areas
- Applied Mathematics
- Discrete Mathematics and Combinatorics