When fast diffusion and reactive growth both induce accelerating invasions

TL;DR

This paper investigates how a combination of fast diffusion and reactive growth can lead to accelerating invasions in monostable equations with a weak Allee effect, expanding understanding of invasion dynamics.

Contribution

It introduces new sub and supersolutions to analyze acceleration caused by combined effects of fast diffusion and reactive growth in monostable equations.

Findings

Acceleration occurs due to combined effects of fast diffusion and reactive growth.

New self-similar solutions are constructed for analysis.

Completes previous understanding by identifying conditions for acceleration.

Abstract

We focus on the spreading properties of solutions of monostable equations with fast diffusion. The nonlinear reaction term involves a weak Allee effect, which tends to slow down the propagation. We complete the picture of [3] by studying the subtle case where acceleration does occur and is induced by a combination of fast diffusion and of reactive growth. This requires the construction of new elaborate sub and supersolutions thanks to some underlying self-similar solutions.