Super-linear propagation for a general, local cane toads model

Christopher Henderson, Benoît Perthame, Panagiotis E. Souganidis

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate a general, local version of the cane toads equation, models the spread of a population structured by unbounded motility. We use the thin-front limit approach of Evans and Souganidis in [Indiana Univ. Math. J., 1989] to obtain a characterization of the propagation in terms of both the linearized equation and a geometric front equation. In particular, we reduce the task of understanding the precise location of the front for a large class of equations to analyzing a much smaller class of Hamilton–Jacobi equations. We are then able to give an explicit formula for the front location in physical space. One advantage of our approach is that we do not use the explicit trajectories along which the population spreads, which was a basis of previous work. Our result allows for large oscillations in the motility.

Original languageEnglish (US)
Pages (from-to)483-509
Number of pages27
JournalInterfaces and Free Boundaries
Volume20
Issue number4
DOIs
StatePublished - 2018
Externally publishedYes

Keywords

  • Cane toads equation
  • Front propagation
  • Long time limits
  • Motility
  • Mutation
  • Reaction diffusion equations
  • Spatial sorting
  • long range

ASJC Scopus subject areas

  • Surfaces and Interfaces

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