Global stability of traveling curved fronts in the Allen-Cahn equations

Hirokazu Ninomiya, Masaharu Taniguchi

Research output: Contribution to journalArticle

52 Citations (Scopus)

Abstract

This paper is concerned with the global stability of a traveling curved front in the Allen-Cahn equation. The existence of such a front is recently proved by constructing supersolutions and subsolutions. In this paper, we introduce a method to construct new subsolutions and prove the asymptotic stability of traveling curved fronts globally in space.

Original languageEnglish
Pages (from-to)819-832
Number of pages14
JournalDiscrete and Continuous Dynamical Systems
Volume15
Issue number3
Publication statusPublished - Jul 2006
Externally publishedYes

Fingerprint

Allen-Cahn Equation
Asymptotic stability
Global Stability
Subsolution
Supersolution
Asymptotic Stability

Keywords

  • Allen-Cahn equation
  • Curved front
  • Global stability
  • Traveling wave

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Global stability of traveling curved fronts in the Allen-Cahn equations. / Ninomiya, Hirokazu; Taniguchi, Masaharu.

In: Discrete and Continuous Dynamical Systems, Vol. 15, No. 3, 07.2006, p. 819-832.

Research output: Contribution to journalArticle

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