Travelling waves for the cane toads equation with bounded traits.

Emeric Bouin 1, 2 Vincent Calvez 1, 2
2 NUMED - Numerical Medicine
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées, Inria Grenoble - Rhône-Alpes
Abstract : In this paper, we study propagation in a nonlocal reaction-diffusion-mutation model describing the invasion of cane toads in Australia. The population of toads is structured by a space variable and a phenotypical trait and the space-diffusivity depends on the trait. We use a Schauder topological degree argument for the construction of some travelling wave solutions of the model. The speed $c^*$ of the wave is obtained after solving a suitable spectral problem in the trait variable. An eigenvector arising from this eigenvalue problem gives the flavor of the profile at the edge of the front. The major difficulty is to obtain uniform $L^\infty$ bounds despite the combination of non local terms and an heterogeneous diffusivity.
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Submitted on : Wednesday, September 18, 2013 - 11:39:55 AM
Last modification on : Tuesday, November 19, 2019 - 12:23:19 PM
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  • HAL Id : hal-00863115, version 1
  • ARXIV : 1309.4755



Emeric Bouin, Vincent Calvez. Travelling waves for the cane toads equation with bounded traits.. 2013. ⟨hal-00863115⟩



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