ncts

In recent years it has been established that, in reaction-diffusion models of monostable type, a favorable environment that flees away from a population density arising from a localized initial condition can in fact improve the spreading speed of this population density. In a simplified Fisher--KPP setting, when the speed of the favorable area is sufficiently small for the population to keep up, then the spreading speed is correctly predicted by the Fisher-KPP speed in this environment. But when the speed is too large for the population to keep up, the Fisher-KPP speed of the second, less favorable environment, is in general only a lower estimate for the spreading speed: the population can be “non-locally pulled” by its exponential tail in the favorable area, even though the distance between this area and the spreading front is linearly increasing in time. The exact spreading speed is given by an explicit formula and at least two methods of proof are known. In this talk I will review some results about non-local pulling in reaction-diffusion systems and equations and then I will present a work in progress in collaboration with Thomas Giletti and Hiroshi Matano.