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 language | English |
|---|---|
| Pages (from-to) | 819-832 |
| Number of pages | 14 |
| Journal | Discrete and Continuous Dynamical Systems |
| Volume | 15 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Jul 2006 |
| Externally published | Yes |
Keywords
- Allen-Cahn equation
- Curved front
- Global stability
- Traveling wave
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics