Global stability of traveling curved fronts in the Allen-Cahn equations
Hirokazu Ninomiya, Masaharu Taniguchi · Discrete and Continuous Dynamical Systems · 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.