Curved fronts of combustion reaction-diffusion equations

Abstract

This paper is concerned with curved fronts of combustion reaction-diffusion equations in ${\mathbb{R}}^N$ $(N\ge 2)$. By mixing finite planar fronts and constructing suitable super- and subsolutions, we prove the existence, uniqueness and stability of polytope-like curved fronts in ${\mathbb{R}}^N$. Besides, we show that these curved fronts are transition fronts.