| Title:
|
Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion (English) |
| Author:
|
Ishiwata, Tetsuya |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
111-119 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
curvature driven motion |
| Keyword:
|
crystalline curvature |
| Keyword:
|
spiral growth |
| MSC:
|
34A26 |
| MSC:
|
34A34 |
| MSC:
|
39A12 |
| MSC:
|
74N05 |
| MSC:
|
82D25 |
| idZBL:
|
Zbl 06486927 |
| idMR:
|
MR3368487 |
| DOI:
|
10.21136/MB.2015.144318 |
| . |
| Date available:
|
2015-06-30T12:09:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144318 |
| . |
| Reference:
|
[1] Gurtin, M. E.: Thermomechanics of Evolving Phase Boundaries in the Plane.Oxford Mathematical Monographs Clarendon Press, Oxford (1993). Zbl 0787.73004, MR 1402243 |
| Reference:
|
[2] Ishiwata, T.: Motion of non-convex polygons by crystalline curvature and almost convexity phenomena.Japan J. Ind. Appl. Math. 25 (2008), 233-253. Zbl 1155.53033, MR 2431681, 10.1007/BF03167521 |
| Reference:
|
[3] Ishiwata, T.: Crystalline motion of spiral-shaped polygonal curves with a tip motion.Discrete Contin. Dyn. Syst., Ser. S 7 (2014), 53-62. Zbl 1273.82076, MR 3082855, 10.3934/dcdss.2014.7.53 |
| . |
