  We establish two integral variational principles for the spreading speed of
the one dimensional reaction diffusion equation with Stefan boundary
conditions. The first principle is valid for monostable reaction terms and the
second principle is valid for arbitrary reaction terms. These principles allow
to obtain several upper and lower bounds for the speed. In particular, we
construct a generalized Zeldovich-Frank-Kamenetskii type lower bound for the
speed and upper bounds in terms of the speed of the standard reaction diffusion
problem. We construct asymptotically exact lower bounds previously obtained by
perturbation theory.
