A MATHEMATICAL-ANALYSIS OF BLOWUP FOR THERMAL-REACTIONS - THE SPATIALLY NON-HOMOGENEOUS CASE

The equations describing the induction period process for a super-critical, high-activation energy thermal explosion in a bounded domain are studied. A formal proof, based on comparison techniques, is used to show that the temperature perturbation becomes unbounded as t approaches t//B less than equivalent to infinity for values of the Frank-Kamenetski parameter delta greater than the critical value. Upper and lower bound estimates for t//B are found by using specified comparison equations. A comparison of these bounds with values of t//B obtained from numerical solution of the basic equations shows that the estimates provide an excellent prediction of the escape time when delta is greater than 2-3 times the critical value. For smaller values of +67,where heat loss is more significant, a better comparison equation is required.