Some remarks on segregation of $k$ species in strongly competing systems

Flavia Lanzara, Eugenio Montefusco
2021 Interfaces and free boundaries (Print)  
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 x/; i D 1; : : : ; k in a domain D with appropriate boundary conditions. Any u i 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 as !
more » ... 1 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.
doi:10.4171/ifb/458 fatcat:3wwq5wjn2fcgtkbk5a44apgkzi