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Existence of reaction-diffusion-convection waves in unbounded strips. (English) Zbl 1075.76058
Summary: Existence of reaction-diffusion-convection waves in unbounded strips is proved in the case of small Rayleigh numbers. In the bistable case the wave is unique, in the monostable case they exist for all speeds greater than the minimal one. The proof uses the implicit function theorem. Its application is based on the Fredholm property, index, and solvability conditions for elliptic problems in unbounded domains.

MSC:
76R99 Diffusion and convection
76V05 Reaction effects in flows
35Q35 PDEs in connection with fluid mechanics
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