Large Time Behaviour of the Solution of a Nonlinear Diffusion Problem in Anthropology (Journal of Mathematical Study, 2018)
In this article we consider a reaction-diffusion model for the spreading offarmers in Europe, which was occupied by hunter-gatherers; this process is known asthe Neolithic agricultural revolution. The spreading of farmers is modelled by a nonlinearporous medium type diffusion equation which coincides with the singular limitof another model for the dispersal of farmers as a small parameter tends to zero. Fromthe ecological viewpoint, the nonlinear diffusion takes into account the populationdensity pressure of the farmers on their dispersal. The interaction between farmersand hunter-gatherers is of the Lotka-Volterra prey-predator type. We show the existenceand uniqueness of a global in time solution and study its asymptotic behaviouras time tends to infinity.