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

Emeric Bouin; Christopher Henderson; Lenya Ryzhik

doi:10.1016/j.matpur.2017.05.015

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

Emeric Bouin, Christopher Henderson, Lenya Ryzhik

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	724-750
Number of pages	27
Journal	Journal des Mathematiques Pures et Appliquees
Volume	108
Issue number	5
DOIs	https://doi.org/10.1016/j.matpur.2017.05.015
State	Published - Nov 2017
Externally published	Yes

Keywords

Front acceleration
Non-local reaction–diffusion equations
Structured populations

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2017.05.015

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title = "Super-linear spreading in local and non-local cane toads equations",

abstract = "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 t3/2. We also get the sharp rate of spreading in a related local model.",

keywords = "Front acceleration, Non-local reaction–diffusion equations, Structured populations",

author = "Emeric Bouin and Christopher Henderson and Lenya Ryzhik",

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AU - Henderson, Christopher

AU - Ryzhik, Lenya

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N2 - 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 t3/2. We also get the sharp rate of spreading in a related local model.

AB - 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 t3/2. We also get the sharp rate of spreading in a related local model.

KW - Front acceleration

KW - Non-local reaction–diffusion equations

KW - Structured populations

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

Abstract

Keywords

ASJC Scopus subject areas

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