A Fisher-KPP model with a fast diffusion line in periodic media

Autor:	Affili, Elisa
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs 35K57 92D25 35B40 35K40 35B53 35B10 35J35
Druh dokumentu:	Working Paper
Popis:	We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different dimensions. Here, we consider for the first time the case of a reaction term depending on a spatial variable in a periodic fashion, which is of great interest for both its mathematical difficulties and for its applications. We derive necessary and sufficient conditions for the survival of the species in terms of the sign of a suitable generalised principal eigenvalue. Moreover, we compare the long time behaviour of a population in the same environment without the fast diffusion line, finding that this element has no impact on the survival chances. Comment: 41 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.14760 Zobrazit plný text záznamu View this record from Arxiv