KPP reaction-diffusion equations with a non-linear loss inside a cylinder

TL;DR

This paper investigates reaction-diffusion systems with flow and non-linear loss inside a cylinder, establishing existence of traveling fronts, minimal speeds, and spreading properties under KPP conditions.

Contribution

It extends the study of reaction-diffusion systems to multi-equation cases with non-linear losses and flow, proving existence of traveling fronts and minimal speeds.

Findings

Existence of traveling and generalized traveling fronts

Identification of a minimal speed for wave propagation

Spreading results for exponentially decaying initial conditions

Abstract

We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.