Existence and global stability of traveling curved fronts in the Allen-Cahn equations

Hirokazu Ninomiya, Masaharu Taniguchi

Research output: Contribution to journalArticle

84 Citations (Scopus)

Abstract

This paper is concerned with existence and stability of traveling curved fronts for the Allen-Cahn equation in the two-dimensional space. By using the supersolution and the subsolution, we construct a traveling curved front, and show that it is the unique traveling wave solution between them. Our supersolution can be taken arbitrarily large, which implies some global asymptotic stability for the traveling curved front.

Original languageEnglish
Pages (from-to)204-233
Number of pages30
JournalJournal of Differential Equations
Volume213
Issue number1
DOIs
Publication statusPublished - Jun 1 2005
Externally publishedYes

Keywords

  • Allen-Cahn equation
  • Curved front
  • Stability
  • Traveling wave

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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