Super-linear propagation for a general, local cane toads model - Archive ouverte HAL Access content directly
Journal Articles Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications Year : 2018

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

Abstract

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 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.
Fichier principal
Vignette du fichier
general_toads.pdf (293.23 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01520145 , version 1 (09-05-2017)
hal-01520145 , version 2 (17-05-2018)

Identifiers

Cite

Christopher Henderson, Benoît Perthame, Panagiotis E Souganidis. Super-linear propagation for a general, local cane toads model. Interfaces and Free Boundaries : Mathematical Analysis, Computation and Applications, 2018, 20 (4), pp.483-509. ⟨10.4171/IFB/409⟩. ⟨hal-01520145v2⟩
669 View
255 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More