Standing Waves in Exothermic Systems

The classical problem of thermal ignition in an infinitely extending reactive slab is revisited. In Frank-Kamenetskii's formulation the temperature distribution in the horizontal direction is assumed uniform and the critical value of the parameter δ such that any excess in δ leads to thermal ignition is found. A strict analysis of the original problem shows that an additional stationary state exists in the form of a standing wave of reaction. Although the newly discovered solution is unstable, it plays an important role in determining the critical local disturbance of the temperature field necessary to lead to thermal ignition.