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Asymptotic Spreading in a Competition System with Nonlocal Dispersal
Xiaoming Yang,Guo Lin,Jianing Yang
Keywords:Nonmonotone system; upper and lower solutions; auxiliary system.
Abstract:
      This paper is concerned with the long time behavior of a competition system with nonlocal dispersal. When the initial conditions of both unknown functions satisfy proper decay behavior, we obtain the rough spreading speed of one unknown function and show the upper and lower bounds of spreading speed of another unknown function. Moreover, a numerical example is given to illustrate our analytic results. Our results imply that both the linear part and nonlinear part in reaction terms may affect the spreading speeds. Moreover, in such a competitive system with constant coefficients, we may observe the propagation terraces in some component.