Singular limit for a reaction-diffusion-ODE system in a neolithic transition model

Ján Eliaš, Danielle Hilhorst, Masayasu Mimura, Yoshihisa Morita
2021 Journal of Differential Equations  
A reaction-diffusion-ODE model for the Neolithic spread of farmers in Europe has been recently proposed in [7] . In this model, farmers are assumed to be divided into two subpopulations according to a mobility rule, namely, into sedentary and migrating farming populations. The conversion between the farming subpopulations depends on the total density of farmers and it is superimposed on the classical Lotka-Volterra competition model, so that it is described by a three-component
more » ... n-ODE system. In this article we consider a singular limit problem when the conversion rate tends to infinity and prove under appropriate conditions that solutions of the three component system converge to solutions of a two-component system with a linear diffusion and nonlinear degenerate diffusion.
doi:10.1016/j.jde.2021.05.044 fatcat:otdhxx26mbhbnntybwyg6wdvhe