Super-linear spreading in local bistable cane toads equations

Abstract

In this paper, we study the influence of an Allee effect on the spreading rate in a local reaction-diffusion-mutation equation modelling the invasion of cane toads in Australia. We are, in particular, concerned with the case when the diffusivity can take unbounded values. We show that the acceleration feature that arises in this model with a Fisher-KPP, or monostable, non-linearity still occurs when this non-linearity is instead bistable, despite the fact that this kills the small populations. This is in stark contrast to the work of Alfaro, Gui-Huan, and Mellet-Roquejoffre-Sire in related models, where the change to a bistable non-linearity prevents acceleration.

References in corpus (5)

• On a model of a population with variable motility
• Propagation of solutions to the Fisher-KPP equation with slowly decaying initial data
• Existence of self-accelerating fronts for a non-local reaction-diffusion equations
• Slowing Allee effect vs. accelerating heavy tails in monostable reaction diffusion equations
• Gradient estimates and symmetrization for Fisher-KPP front propagation with fractional diffusion