Mathematical modeling study demonstrates the existence and uniqueness of traveling fronts in reactive jet autoignition, indicating a stable mechanism for flame propagation.
We consider a one-dimensional reaction-diffusion model with a piecewise continuous reaction term that describes the propagation of autoignition fronts in reactive co-flow jets within a certain parametric regime. The model is reduced to a free boundary problem with two interfaces. It is shown that this problem admits a permanent traveling front solution which is unique up to translation. The result is obtained using a dynamical system approach employing the stable manifold theorem and the Melnikov integral as the main tools.
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Ma et al. (2026) studied this question.
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