On the existence of cylindrically symmetric traveling fronts of fractional Allen-Cahn equation in $\mathbb{R}^{3}$

Abstract

This paper is concerned with the existence of cylindrically symmetric traveling fronts for bistable fractional Allen-Cahn equation in $\mathbb{R}^{3}$. By constructing a sequence of pyramidal traveling fronts and taking its limit, we obtain a traveling front with cylindrically symmetric type.