Asymptotic behaviour of the solution of a nonlinear diffusion problem in anthropology

Jeudi 7 juin 2018 14:15-15:15 - Jan Elias - University of Graz

Résumé : In this talk we consider a reaction-diffusion model for the spreading of farmers in Europe, which was occupied by hunter-gatherers ; this process is known as the Neolithic agricultural revolution. The spreading of farmers is modelled by a non- linear porous medium type diffusion equation which coincides with the singular limit of another model for the dispersal of farmers as a small parameter tends to zero. From the ecological viewpoint, the nonlinear diffusion takes into account the population density pressure of the farmers on their dispersal. The interaction between farmers and hunter-gatherers is of the Lotka-Volterra prey-predator type. We show the existence and uniqueness of a global in time solution and study its asymptotic behaviour as time tends to infinity.

Asymptotic behaviour of the solution of a nonlinear diffusion problem in anthropology  Version PDF