FINITE-TIME BLOW-UP IN REACTION-DIFFUSION EQUATIONS

The reaction-diffusion equation u(t) = DELTAu(m) + f(u), with f(u) a p olynomial or exponential function of u, is considered. Upper and lower bounds, numerical routines and similarity solutions are all used to d iscuss the phenomena of finite-time blow-up. In particular, the simila rity solution for f(u) = u(m) provides evidence that the set of blow-u p points does not necessarily have zero measure. Critical conditions f or varying m are found numerically.