SPEED OF FRONTS OF THE REACTION-DIFFUSION EQUATION

We study the speed of propagation of fronts for the scalar reaction-di ffusion equation u(t) = u(xx) + f(u) with f(0) = f(1) = 0. We give a n ew integral variational principle for the speed of fronts joining the state u = 1 to u = 0. No assumptions are made on the reaction term flu ) other than those needed to guarantee the existence of the front. The refore our results apply to the classical case f > 0 in (0, 1), to the bistable ease, and to cases in which f has more than one internal zer o in (0, 1).