Spreading speeds of random KPP equations with nonlocal diffusion

The long time behavior of random KPP equations with nonlocal diffusion is investigated in this paper. The stability of the positive constant equilibrium solution is established for random KPP equations, and the spreading speed property is obtained for the random KPP equation with nonlocal diffusion by means of the comparison principle and auxiliary systems. Our theoretical results can be applied to two generalized KPP models, in which the take-over property of the lattice KPP with a random coefficient is obtained.