M. Belk, B. Kazmierczak, V. Volpert, "Existence of reaction-diffusion-convection waves in unbounded strips", International Journal of Mathematics and Mathematical Sciences, vol. 2005, Article ID 545476, 25 pages, 2005. https://doi.org/10.1155/IJMMS.2005.169
Existence of reaction-diffusion-convection waves in unbounded strips
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.
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