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Spreading speeds for the predator-prey system with nonlocal dispersal. (English) Zbl 1486.35121

This paper is concerned with the propagation properties of solutions of the predator-prey system with nonlocal dispersal. More specifically, authors explored the spreading speeds of the predator and the prey in two different situations, namely, the predator spreads faster than the prey and the predator spreads slower than the prey. The main methods are the comparison principle of the scalar equation and the method of upper and lower solutions. Furthermore, authors proved that the predator and the prey will eventually coexist by constructing a suitable Lyapunov functional. Finally, some numerical simulations are given to illustrate the results.

MSC:

35C07 Traveling wave solutions
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
92D25 Population dynamics (general)
35B51 Comparison principles in context of PDEs
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