Super-linear spreading in local bistable cane toads equations

In this paper, we study the influence of an Allee effect on the spreading rate in a local reaction-diffusion-mutation equation modeling 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, nonlinearity still occurs when this nonlinearity 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 nonlinearity prevents acceleration.