### 抄録

The asymptotic behavior of solutions to an anisotropic crystalline motion is investigated. In this motion, a solution polygon changes the shape by a power of crystalline curvature in its normal direction and develops singularity in a finite time. At the final time, two types of singularity appear: one is a single point-extinction and the other is degenerate pinching. We will discuss the latter case of singularity and show the exact blow-up rate for a fast blow-up or a type 2 blow-up solution which arises in an equivalent blow-up problem.

元の言語 | English |
---|---|

ページ（範囲） | 2069-2090 |

ページ数 | 22 |

ジャーナル | Discrete and Continuous Dynamical Systems- Series A |

巻 | 34 |

発行部数 | 5 |

DOI | |

出版物ステータス | Published - 2014 5 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis

### これを引用

**A fast blow-Up solution and degenerate pinching arising in an anisotropic crystalline motion.** / Ishiwata, Tetsuya; Yazaki, Shigetoshi.

研究成果: Article

*Discrete and Continuous Dynamical Systems- Series A*, 巻. 34, 番号 5, pp. 2069-2090. https://doi.org/10.3934/dcds.2014.34.2069

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TY - JOUR

T1 - A fast blow-Up solution and degenerate pinching arising in an anisotropic crystalline motion

AU - Ishiwata, Tetsuya

AU - Yazaki, Shigetoshi

PY - 2014/5

Y1 - 2014/5

N2 - The asymptotic behavior of solutions to an anisotropic crystalline motion is investigated. In this motion, a solution polygon changes the shape by a power of crystalline curvature in its normal direction and develops singularity in a finite time. At the final time, two types of singularity appear: one is a single point-extinction and the other is degenerate pinching. We will discuss the latter case of singularity and show the exact blow-up rate for a fast blow-up or a type 2 blow-up solution which arises in an equivalent blow-up problem.

AB - The asymptotic behavior of solutions to an anisotropic crystalline motion is investigated. In this motion, a solution polygon changes the shape by a power of crystalline curvature in its normal direction and develops singularity in a finite time. At the final time, two types of singularity appear: one is a single point-extinction and the other is degenerate pinching. We will discuss the latter case of singularity and show the exact blow-up rate for a fast blow-up or a type 2 blow-up solution which arises in an equivalent blow-up problem.

KW - Blow-up core

KW - Blow-up rate

KW - Crystalline motion

KW - Degenerate pinching

UR - http://www.scopus.com/inward/record.url?scp=84886555724&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886555724&partnerID=8YFLogxK

U2 - 10.3934/dcds.2014.34.2069

DO - 10.3934/dcds.2014.34.2069

M3 - Article

AN - SCOPUS:84886555724

VL - 34

SP - 2069

EP - 2090

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 5

ER -