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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/56117 |
| Acceso en línea: | http://hdl.handle.net/11441/56117 https://doi.org/10.1016/j.jde.2017.02.012 |
| Access Level: | acceso abierto |
| Palabra clave: | Non-linear diffusion Bifurcation Sub-supersolution method Large solutions Population dynamics |
| Sumario: | 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. |
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