August  2006, 15(3): 819-832. doi: 10.3934/dcds.2006.15.819

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

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  May 2005 Revised  December 2005 Published  April 2006

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.
Citation: Hirokazu Ninomiya, Masaharu Taniguchi. Global stability of traveling curved fronts in the Allen-Cahn equations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 819-832. doi: 10.3934/dcds.2006.15.819
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