Abstract
The behavior of polygonal curves with asymptotic lines to crys- talline motion with the bulk e ect is discussed. We show sufficient conditions for global existence of the solutions and characterize facet-extinction patterns. We also show the eventual monotonicity of shape of the solution curves, that is, the solutions become V-shaped in finite time.
| Original language | English |
|---|---|
| Pages (from-to) | 865-873 |
| Number of pages | 9 |
| Journal | Discrete and Continuous Dynamical Systems - Series S |
| Volume | 4 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2011 Aug |
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Keywords
- Crystalline curvature
- Crystalline motion
- Eventual monotonicity
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Discrete Mathematics and Combinatorics
Cite this
On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect. / Ishiwata, Tetsuya.
In: Discrete and Continuous Dynamical Systems - Series S, Vol. 4, No. 4, 08.2011, p. 865-873.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect
AU - Ishiwata, Tetsuya
PY - 2011/8
Y1 - 2011/8
N2 - The behavior of polygonal curves with asymptotic lines to crys- talline motion with the bulk e ect is discussed. We show sufficient conditions for global existence of the solutions and characterize facet-extinction patterns. We also show the eventual monotonicity of shape of the solution curves, that is, the solutions become V-shaped in finite time.
AB - The behavior of polygonal curves with asymptotic lines to crys- talline motion with the bulk e ect is discussed. We show sufficient conditions for global existence of the solutions and characterize facet-extinction patterns. We also show the eventual monotonicity of shape of the solution curves, that is, the solutions become V-shaped in finite time.
KW - Crystalline curvature
KW - Crystalline motion
KW - Eventual monotonicity
UR - http://www.scopus.com/inward/record.url?scp=84864479518&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84864479518&partnerID=8YFLogxK
U2 - 10.3934/dcdss.2011.4.865
DO - 10.3934/dcdss.2011.4.865
M3 - Article
VL - 4
SP - 865
EP - 873
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
SN - 1937-1632
IS - 4
ER -