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

Emeric Bouin, Christopher Henderson, Lenya Ryzhik

Research output: Contribution to journalArticlepeer-review

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

Original languageEnglish (US)
Pages (from-to)724-750
Number of pages27
JournalJournal des Mathematiques Pures et Appliquees
Volume108
Issue number5
DOIs
StatePublished - Nov 2017
Externally publishedYes

Keywords

  • Front acceleration
  • Non-local reaction–diffusion equations
  • Structured populations

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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