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This paper considers the spreading speed of cooperative nonlocal dispersalsystem with irreducible reaction functions and non-uniform initial data. Herethe non-uniformity means that all components of initial data decayexponentially but their decay rates are different. It is well-known that in amonostable reaction-diffusion or nonlocal dispersal equation, different decayrates of initial data yield different spreading speeds. In this paper, we showthat due to the cooperation and irreducibility of reaction functions, allcomponents of the solution with non-uniform initial data will possess a uniformspreading speed which non-increasingly depends only on the smallest decay rateof initial data. The nonincreasing property of the uniform spreading speedfurther implies that the component with the smallest decay rate can acceleratethe spatial propagation of other components. In addition, all the methods inthis paper can be carried over to the cooperative system with classicaldiffusion (i.e. random diffusion).

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