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Traveling wavefronts for delayed reaction-diffusion systems via a fixed point theorem. (English) Zbl 0988.34053

Summary: By using Schauder’s fixed-point theorem, the author proves some existence results for traveling wavefronts to reaction-diffusion systems with quasimonotonicity reactions. More precisely, he reduces the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution, which are easy to construct in practice. Finally, to illustrate the main results, he studies the existence of traveling wavefronts for a delayed predator-prey model with diffusion as well as the reaction-diffusion system with the well-known Belousov-Zhabotinskii reaction. The obtained results improve the existing ones.

MSC:

34K10 Boundary value problems for functional-differential equations
35K57 Reaction-diffusion equations
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