Refuge versus dispersion in the logistic equation

In this paper we consider a logistic equation with nonlinear diffusion arising in population dynamics. In this model, there exists a refuge where the species grows following a Malthusian law and, in addition, there exists also a non-linear diffusion representing a repulsive dispersion of the species...

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Bibliographic Details
Authors: Cintra da Silva, Willian, Morales Rodrigo, Cristian, Suárez Fernández, Antonio
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2017
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/56117
Online Access:http://hdl.handle.net/11441/56117
https://doi.org/10.1016/j.jde.2017.02.012
Access Level:Open access
Keyword:Non-linear diffusion
Bifurcation
Sub-supersolution method
Large solutions
Population dynamics
Description
Summary:In this paper we consider a logistic equation with nonlinear diffusion arising in population dynamics. In this model, there exists a refuge where the species grows following a Malthusian law and, in addition, there exists also a non-linear diffusion representing a repulsive dispersion of the species. We prove existence and uniqueness of positive solution and study the behavior of this solution with respect to the parameter λ, the growth rate of the species. Mainly, we use bifurcation techniques, the sub-supersolution method and a construction of appropriate large solutions.