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Super-linear spreading in local and non-local cane toads equations

Bouin, Emeric; Henderson, Christopher; Ryzhik, Lenya (2017), Super-linear spreading in local and non-local cane toads equations, Journal de mathématiques pures et appliquées, 108, 5, p. 724-750. 10.1016/j.matpur.2017.05.015

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01248264
Date
2017
Journal name
Journal de mathématiques pures et appliquées
Volume
108
Number
5
Publisher
Bachelier
Pages
724-750
Publication identifier
10.1016/j.matpur.2017.05.015
Metadata
Show full item record
Author(s)
Bouin, Emeric
Henderson, Christopher
Ryzhik, Lenya
Abstract (FR)
Dans cet article, nous prouvons un résultat de propagation accélérée pour une équation de réaction–diffusion–mutation non locale qui modélise l'invasion de crapauds buffles en Australie. La population de crapauds est structurée en phénotype, et ce phénotype modifie le coefficient de diffusion spatiale. Nous considérons le cas de diffusivités non bornées, et nous prouvons que le taux de propagation est t32. Nous obtenons aussi le taux précis d'accélération pour un modèle local associé.
Abstract (EN)
In this paper, we show super-linear propagation in a nonlocal reaction-diffusion-mutation equation modeling the invasion of cane toads in Australia that has attracted attention recently from the mathematical point of view. The population of toads is structured by a phenotypical trait that governs the spatial diffusion. In this paper, we are concerned with the case when the diffusivity can take unbounded values, and we prove that the population spreads as $t^{3/2}$. We also get the sharp rate of spreading in a related local model.
Subjects / Keywords
Structured populations; Non-local reaction–diffusion equations; Front acceleration

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