Évènement

We present a City-Road reaction-diffusion model on the one-dimensional lattice, where « cities » are interconnected by a transportation network such as roads, railways, or rivers. The model describes the spread of epidemics or biological invasions along the roads connecting cities. We first establish the well-posedness of the Cauchy problem and analyze the long time behavior of solutions. To understand the effect of rapid movement along the roads, we investigate the fast diffusion regime with $dto+infty$. In this regime, we derive a novel asymptotic system that differs from the classical discrete Fisher-KPP equation but exhibits similar propagation properties. We rigorously prove the existence and uniqueness of positive stationary solution and describe long time bahavior. These results allow us to characterize the asymptotic spreading speed and obtain its expansion in the large diffusion limit. In addition, we investigated the asymptotic behavior of the propagation speed for the two regimes