Geodesic
Super-linear propagation for a general, local cane toads model
Christopher Henderson1 ; Benoît Perthame2 ; Panagiotis E. Souganidis1
1The University of Chicago, USA
2Sorbonne Université, Université Paris Diderot, France
Interfaces and free boundaries, Tome 20 (2018) no. 4, pp. 483-509

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DOI

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.
DOI : 10.4171/ifb/409
Classification : 35-XX, 76-XX
Mots-clés : Reaction diffusion equations; long range, long time limits; motility; cane toads equation; mutation; spatial sorting, front propagation

Christopher Henderson  1   ; Benoît Perthame  2   ; Panagiotis E. Souganidis  1

1 The University of Chicago, USA
2 Sorbonne Université, Université Paris Diderot, France 
Christopher Henderson; Benoît Perthame; Panagiotis E. Souganidis. Super-linear propagation for a general, local cane toads model. Interfaces and free boundaries, Tome 20 (2018) no. 4, pp. 483-509. doi: 10.4171/ifb/409
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