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Monotone wavefronts for partially degenerate reaction-diffusion systems. (English) Zbl 1180.35275

Summary: This paper is devoted to the study of monotone wavefronts for cooperative and partially degenerate reaction-diffusion systems. The existence of monostable wavefronts is established via the vector-valued upper and lower solutions method. It turns out that the minimal wave speed of monostable wavefronts coincides with the spreading speed. The existence of bistable wavefronts is obtained by the vanishing viscosity approach combined with the properties of spreading speeds in the monostable case.

MSC:

35K45 Initial value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35B20 Perturbations in context of PDEs
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