Spatial segregation occurs in population dynamics when k species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of k differential equations in a domain D with appropriate boundary conditions. Any ui represents a population density and the parameter determines the interaction strength between the populations. The purpose of this paper is to study the geometry of the limiting configuration on a planar domain for any number of species. If k is even we show that some limiting configurations are strictly connected to the solution of a Dirichlet problem for the Laplace equation.
Some remarks on segregation of k species in strongly competing systems / Lanzara, Flavia; Montefusco, Eugenio. - In: INTERFACES AND FREE BOUNDARIES. - ISSN 1463-9963. - 23:3(2021), pp. 403-419. [10.4171/IFB/458]
Some remarks on segregation of k species in strongly competing systems
FLAVIA LANZARA;EUGENIO MONTEFUSCO
2021
Abstract
Spatial segregation occurs in population dynamics when k species interact in a highly competitive way. As a model for the study of this phenomenon, we consider the competition-diffusion system of k differential equations in a domain D with appropriate boundary conditions. Any ui represents a population density and the parameter determines the interaction strength between the populations. The purpose of this paper is to study the geometry of the limiting configuration on a planar domain for any number of species. If k is even we show that some limiting configurations are strictly connected to the solution of a Dirichlet problem for the Laplace equation.| File | Dimensione | Formato | |
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