### 抄録

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.

元の言語 | English |
---|---|

記事番号 | A111 |

ページ（範囲） | 111-119 |

ページ数 | 9 |

ジャーナル | Mathematica Bohemica |

巻 | 140 |

発行部数 | 2 |

出版物ステータス | Published - 2015 |

### ASJC Scopus subject areas

- Mathematics(all)

### これを引用

*Mathematica Bohemica*,

*140*(2), 111-119. [A111].

**Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion.** / Ishiwata, Tetsuya.

研究成果: Article

*Mathematica Bohemica*, 巻. 140, 番号 2, A111, pp. 111-119.

}

TY - JOUR

T1 - Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion

AU - Ishiwata, Tetsuya

PY - 2015

Y1 - 2015

N2 - 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.

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.

KW - Crystalline curvature

KW - Curvature driven motion

KW - Spiral growth

UR - http://www.scopus.com/inward/record.url?scp=84942314871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84942314871&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84942314871

VL - 140

SP - 111

EP - 119

JO - Mathematica Bohemica

JF - Mathematica Bohemica

SN - 0862-7959

IS - 2

M1 - A111

ER -