Critical behavior of an ignition model in chemical combustion
A model for the hot slab ignition problem is analyzed to determine critical conditions. The system is said to be supercritical if the solution of the reduced perturbation problem blows up in small finite time or subcritical if the blow-up time is large. Comparison principles for integral equations are used to construct upper and lower solutions of the equation. All solutions depend on two parameters {epsilon}{sup {minus}1}, the Zeldovitch number and lambda, the scaled hot slab size. Upper and lower bounds on a 'critical' curve {lambda}{sub c} ({epsilon}) in the ({epsilon}, {lambda}) plane, separating the supercritical from the subcritical region, are derived based upon the lower and upper solution behavior. Numerical results confirm the parameter space analysis. 13 refs.