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

Hirokazu Ninomiya; Masaharu Taniguchi

doi:10.3934/dcds.2006.15.819

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2006, Volume 15, Issue 3: 819-832. Doi: 10.3934/dcds.2006.15.819

This issue Previous Article Hyperbolic invariant sets with positive measures Next Article On the Euler equation for minimal geodesics on Riemannian manifoldshaving discontinuous metrics

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

Hirokazu Ninomiya^1, and
Masaharu Taniguchi^2,

1.
Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194
2.
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552

Received: April 30, 2005

Revised: November 30, 2005

Published: August 2006

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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.

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Mathematics Subject Classification: 35K57, 35B35.

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