Convergence to V-shaped fronts in curvature flows for spatially non-decaying initial perturbations

Mitsunori Nara, Masaharu Taniguchi

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This paper is concerned with the long time behavior for evolution of a curve governed by a curvature flow with constant driving force in the two-dimensional space. This problem has two types of traveling waves: traveling lines and V-shaped fronts, except for stationary circles. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the x-axis. In this paper, we consider the uniform convergence of curves to the V-shaped fronts. Convergence results for a class of spatially non-decaying initial perturbations are established. Our results hold true with no assumptions on the smallness of given perturbations.

Original languageEnglish
Pages (from-to)137-156
Number of pages20
JournalDiscrete and Continuous Dynamical Systems
Volume16
Issue number1
DOIs
Publication statusPublished - Sep 2006
Externally publishedYes

Keywords

  • Convergence
  • Curvature flow
  • Traveling waves

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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