| Popis: |
In this paper, we investigate the spreading properties of solutions of the Aoki-Shida-Shigesada model. This model is a three-component reaction-diffusion system that delineates the geographical expansion of an initially localized population of farmers into a region occupied by hunter-gatherers. By considering the scenario where farmers and hunter-gatherers possess identical motility, Aoki et al. previously concluded, through numerical simulations and some formal linearization arguments, that there are four different types of spreading behaviors depending on the parameter values. In this paper, we concentrate on the general case for which farmers and hunter-gatherers possess different motility. By providing more sophisticated estimates, we not only theoretically justify the spreading speed of the Aoki-Shida-Shigesada model, but also establish sharp estimates for the long-time behaviors of solutions. These estimates enable us to validate all four types of spreading behaviors observed by Aoki et al.. |
