Abstract#x2013;A one-dimensional model describing a self-sustaining reaction wave moving through a unidirectional periodic flow field is proposed and studied numerically. In the case of zero diffusivity of the deficient reactant the reaction wave undergoes partial extinction, as a result of which a considerable portion of the original premixture remains unconsumed. For long-wavelength fields within a certain range of the flow intensities the system exhibits a peculiar nonuniqueness of possible propagation regimes. The transition from one regime to another occurs in a manner of hysteresis.
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