THE UNIFORM SPREADING SPEED IN COOPERATIVE SYSTEMS WITH NON-UNIFORM INITIAL DATA

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.

Automated summary

This paper investigates the spreading speed of cooperative nonlocal dispersal systems with irreducible reaction functions and non-uniform initial data. The non-uniformity refers to the exponential decay of all components of the initial data, but with different decay rates. It has been established that different decay rates of initial data in a monostable reaction-diffusion or nonlocal dispersal equation result in different spreading speeds. The paper demonstrates that due to the cooperation and irreducibility of reaction functions, all components of the solution with non-uniform initial data will have a uniform spreading speed that depends solely on the smallest decay rate of the initial data. The decreasing property of the uniform spreading speed in the smallest decay rate implies that the component with the smallest decay rate can accelerate the spatial propagation of other components.