TY - JOUR
T1 - Super-linear spreading in local and non-local cane toads equations
AU - Bouin, Emeric
AU - Henderson, Christopher
AU - Ryzhik, Lenya
N1 - Funding Information:
The authors wish to thank Vincent Calvez and Sepideh Mirrahimi for fruitful discussions and earlier computations on this problem. LR was supported by NSF grant DMS-1311903 . EB was supported by “ INRIA Programme Explorateur ” and is very grateful to Stanford University for its sunny hospitality during the second semester of the academic year 2014–2015. CH acknowledges the support of the “École normale supérieure de Lyon” for a one-week visit in April 2015. Part of this work was performed within the framework of the LABEX MILYON ( ANR-10-LABX-0070 ) of the “ Université de Lyon ”, within the program “Investissements d'avenir” ( ANR-11-IDEX-0007 ) operated by the French National Research Agency (ANR).
Publisher Copyright:
© 2017 Elsevier Masson SAS
PY - 2017/11
Y1 - 2017/11
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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U2 - 10.1016/j.matpur.2017.05.015
DO - 10.1016/j.matpur.2017.05.015
M3 - Article
AN - SCOPUS:85021998327
VL - 108
SP - 724
EP - 750
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
IS - 5
ER -