Ignition of a Reactive Solid Exposed to a Step in Surface Temperature

The title problem is classical in ignition theory. Here it is solved by an asymptotic analysis in which the nondimensional activation energy is treated as a large parameter. Inert and reactive zones are identified, and a temperature peak develops in the latter during a stage of transition to ignition. A criterion of thermal runaway yields a formally correct asymptotic expansion for the ignition time which agrees with results of numerical integrations if the activation energy is sufficiently large.