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 |
|---|---|
| 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 |
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Keywords
- Crystalline curvature
- Motion by curvature
- Polygonal curves
- Spirals
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Discrete Mathematics and Combinatorics
Cite this
On spiral solutions to generalized crystalline motion with a rotating tip motion. / Ishiwata, Tetsuya.
In: Discrete and Continuous Dynamical Systems - Series S, Vol. 8, No. 5, 01.10.2015, p. 881-888.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On spiral solutions to generalized crystalline motion with a rotating tip motion
AU - Ishiwata, Tetsuya
PY - 2015/10/1
Y1 - 2015/10/1
N2 - 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.
AB - 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.
KW - Crystalline curvature
KW - Motion by curvature
KW - Polygonal curves
KW - Spirals
UR - http://www.scopus.com/inward/record.url?scp=84936768170&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84936768170&partnerID=8YFLogxK
U2 - 10.3934/dcdss.2015.8.881
DO - 10.3934/dcdss.2015.8.881
M3 - Article
AN - SCOPUS:84936768170
VL - 8
SP - 881
EP - 888
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
SN - 1937-1632
IS - 5
ER -