CRITICAL INITIAL CONDITIONS FOR THERMAL IGNITION

In the conductive theory of thermal ignition, there is a practically i mportant region of parameter space where the heat conduction partial d ifferential equation with a nonlinear (Arrhenius) heat generation term displays two attractors. Their basins of attraction (particularly tha t of the minimal solutions) are of great practical importance. Good es timates for the latter region are obtained by a method of spatial aver aging of the nonlinear term which give very small errors for large cla sses of initial conditions, provided the latter are not too 'spikey.' For 'hot spot' type initial conditions the method still works and give s satisfactory estimates. The bound is focussed on the critical initia l energy.