Shock-induced ignition is considered for a three-step chain-branching mechanism at large activationenergies. The nature of the ignition process depends critically on the magnitude of the initial post-shocktemperature relative to the chain-branching cross-over temperature. For the limits examined, the inductionregion is preceded by an exponentially weak initiation zone that provides relevant initial conditionsfor the induction phase. When the initial post-shock temperature is sufficiently close to the chain-branchingtemperature, ignition is characterized by logarithmic singular behaviors in the pressure and temperatureperturbations and the structure has some similarities with the one-step chemistry problem.However, for larger initial post-shock temperatures, the logarithmic singularities are replaced by lineartemporal growth. Suitable non-linear Clarke equations are deduced for both of these cases and numericalsolutions are presented.
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