Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
Mathematica Bohemica (2015)
- Volume: 140, Issue: 2, page 111-119
- ISSN: 0862-7959
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topIshiwata, Tetsuya. "Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion." Mathematica Bohemica 140.2 (2015): 111-119. <http://eudml.org/doc/271657>.
@article{Ishiwata2015,
abstract = {We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never occurs. Finally, we show that spiral-shaped solutions exist globally in time.},
author = {Ishiwata, Tetsuya},
journal = {Mathematica Bohemica},
keywords = {curvature driven motion; crystalline curvature; spiral growth},
language = {eng},
number = {2},
pages = {111-119},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion},
url = {http://eudml.org/doc/271657},
volume = {140},
year = {2015},
}
TY - JOUR
AU - Ishiwata, Tetsuya
TI - Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 2
SP - 111
EP - 119
AB - We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never occurs. Finally, we show that spiral-shaped solutions exist globally in time.
LA - eng
KW - curvature driven motion; crystalline curvature; spiral growth
UR - http://eudml.org/doc/271657
ER -
References
top- Gurtin, M. E., Thermomechanics of Evolving Phase Boundaries in the Plane, Oxford Mathematical Monographs Clarendon Press, Oxford (1993). (1993) Zbl0787.73004MR1402243
- Ishiwata, T., 10.1007/BF03167521, Japan J. Ind. Appl. Math. 25 (2008), 233-253. (2008) Zbl1155.53033MR2431681DOI10.1007/BF03167521
- Ishiwata, T., 10.3934/dcdss.2014.7.53, Discrete Contin. Dyn. Syst., Ser. S 7 (2014), 53-62. (2014) Zbl1273.82076MR3082855DOI10.3934/dcdss.2014.7.53
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