TRAVELING WAVES IN A NONLOCAL DISPERSAL

This paper is concerned with the traveling wave solutions for a class of predator-prey model with nonlocal dispersal. By adopting the truncation method, we use Schauder's fixed-point theorem to obtain the existence of traveling waves connecting the semi-trivial equilibrium to non-trivial leftover concentrations for c > c(*), in which c(*) is the minimal wave speed. Meanwhile, through the limiting approach and the delicate analysis, we establish the existence of traveling wave solutions with the critical speed. Finally, we show the nonexistence of traveling waves for 0 < c < c(*) by the characteristic equation corresponding to the linearization of original system at the semi-trivial equilibrium. Throughout the whole paper, we need to overcome the difficulties brought by the nonlocal dispersal and the non-preserving of system itself.