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Wave propagation for a class of non-local dispersal non-cooperative systems. (English) Zbl 1465.35282

Summary: This paper is concerned with the travelling waves for a class of non-local dispersal non-cooperative system, which can model the prey-predator and disease-transmission mechanism. By the Schauder’s fixed-point theorem, we first establish the existence of travelling waves connecting the semi-trivial equilibrium to non-trivial leftover concentrations, whose bounds are deduced from a precise analysis. Further, we characterize the minimal wave speed of travelling waves and obtain the non-existence of travelling waves with slow speed. Finally, we apply the general results to an epidemic model with bilinear incidence for its propagation dynamics.

MSC:

35K57 Reaction-diffusion equations
35C07 Traveling wave solutions
35R09 Integro-partial differential equations
35K45 Initial value problems for second-order parabolic systems
35K58 Semilinear parabolic equations
47G20 Integro-differential operators
92D25 Population dynamics (general)
45F05 Systems of nonsingular linear integral equations
45A05 Linear integral equations
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