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Super-linear spreading in local bistable cane toads equations

Bouin, Emeric; Henderson, Christopher (2017), Super-linear spreading in local bistable cane toads equations, Nonlinearity, 30, 4, p. n°1356. 10.1088/1361-6544/aa5d65

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01293988
Date
2017
Journal name
Nonlinearity
Volume
30
Number
4
Publisher
IOP Publishing
Pages
n°1356
Publication identifier
10.1088/1361-6544/aa5d65
Metadata
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Author(s)
Bouin, Emeric
Henderson, Christopher
Abstract (EN)
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.
Subjects / Keywords
PDE

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