Curved fronts of combustion reaction-diffusion equations

TL;DR

This paper investigates the existence, uniqueness, and stability of curved, polytope-like fronts in combustion reaction-diffusion equations in multiple dimensions, demonstrating they are transition fronts.

Contribution

It introduces a novel method combining finite planar fronts and super- and subsolutions to establish properties of curved fronts in reaction-diffusion systems.

Findings

Existence of polytope-like curved fronts in 

Uniqueness and stability of these fronts

Curved fronts are confirmed as transition fronts

Abstract

This paper is concerned with curved fronts of combustion reaction-diffusion equations in $\mathbb{R}^N$ $(N\geq2)$. 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.