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

Tetsuya Ishiwata, Shigetoshi Yazaki

研究成果: Article

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
34
発行部数5
DOI
出版物ステータスPublished - 2014 5

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Crystalline materials

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

これを引用

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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.

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