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Front propagation in periodic excitable media. (English) Zbl 1024.37054
This paper is devoted to the analysis of some front propagation phenomena for a class of reaction-diffusion-advection equations in various periodic domains. Various existence, uniqueness, and monotonicity results are proved for two classes of reaction terms. First, for a combustion-type nonlinearity, it is proved that the pulsating travelling front exists and that its speed is unique. Secondly, they consider one class of monostable nonlinearity that arises either in combustion or biological models.

MSC:
37N99 Applications of dynamical systems
35K57 Reaction-diffusion equations
35Q80 Applications of PDE in areas other than physics (MSC2000)
35B10 Periodic solutions to PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
80A25 Combustion
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