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

Christopher Henderson (1) , Benoît Perthame (2, 3, 4, 5) , Panagiotis E Souganidis (1)

1 Department of Mathematics [Chicago]
2 UPD7 - Université Paris Diderot - Paris 7
3 SU - Sorbonne Université
4 MAMBA - Modelling and Analysis for Medical and Biological Applications
5 LJLL - Laboratoire Jacques-Louis Lions

In this article, we investigate a general local version of the cane toads equation, which 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 and a geometric front equations. Our result allows for large oscillations in the motility.

Domaines: Equations aux dérivées partielles [math.AP]

Christopher Henderson, Benoît Perthame, Panagiotis E Souganidis. Super-linear propagation for a general, local cane toads model. 2017. ⟨hal-01520145v1⟩