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

Tetsuya Ishiwata, Shigetoshi Yazaki

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)2069-2090
Number of pages22
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume34
Issue number5
DOIs
Publication statusPublished - 2014 May

Keywords

  • Blow-up core
  • Blow-up rate
  • Crystalline motion
  • Degenerate pinching

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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