JournalsifbVol. 20, No. 4pp. 483–509

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

  • Christopher Henderson

    The University of Chicago, USA
  • Benoît Perthame

    Sorbonne Université, Université Paris Diderot, France
  • Panagiotis E. Souganidis

    The University of Chicago, USA
Super-linear propagation for a general, local cane toads model cover

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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.

Cite this article

Christopher Henderson, Benoît Perthame, Panagiotis E. Souganidis, Super-linear propagation for a general, local cane toads model. Interfaces Free Bound. 20 (2018), no. 4, pp. 483–509

DOI 10.4171/IFB/409