We study the behaviour of steady-state solutions of a two-component flame filament system subject to chaotic mixing. This system exhibits a saddle-node bifurcation at a critical Damköhler number. We analyze the system through a one-dimensional phenomenological lamellar model. We present a nonperturbative technique, which allows us to describe the behaviour of the reduced lamellar model near the saddle node bifurcation. The influence of the Lewis number on the solution behaviour is investigated. We present a simple empirical formula for the wave speed valid for large Damköhler and large Lewis numbers. This formula allows us to describe the solution far away from the bifurcation. Numerical simulations show good agreement with the results.
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