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The system of two parabolic PDEs is characterized by a free interface at which ignition temperature $\\Theta_i$ is reached. We turn the model to a fully nonlinear problem in a fixed domain. When the Lewis number is large, we define a bifurcation parameter $m=\\Theta_i/(1-\\Theta_i)$ and a perturbation parameter $\\varepsilon= 1/{\\rm Le}$. 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