Abstract
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.
Original language | English |
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Pages (from-to) | 881-888 |
Number of pages | 8 |
Journal | Discrete and Continuous Dynamical Systems - Series S |
Volume | 8 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2015 Oct 1 |
Keywords
- Crystalline curvature
- Motion by curvature
- Polygonal curves
- Spirals
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics