The uniform spreading speed in cooperative systems with non-uniform initial data

Abstract

This paper considers the spreading speed of cooperative nonlocal dispersal systems with irreducible reaction functions and non-uniform initial data. Here the non-uniformity means that all components of initial data decay exponentially but their decay rates are different. It is well-known that in a monostable reaction-diffusion or nonlocal dispersal equation, different decay rates of initial data yield different spreading speeds. In this paper, we show that due to the cooperation and irreducibility of reaction functions, all components of the solution with non-uniform initial data will possess a uniform spreading speed which decreasingly depends only on the smallest decay rate of initial data. The decreasing property of the uniform spreading speed in the smallest decay rate further implies that the component with the smallest decay rate can accelerate the spatial propagation of other components.