  We consider the problem of the speed selection mechanism for the one
dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been
rigorously shown by Aronson and Weinberger that for a wide class of functions
$f$, sufficiently localized initial conditions evolve in time into a monotonic
front which propagates with speed $c^*$ such that $2 \sqrt{f'(0)} \leq c^* < 2
\sqrt{\sup(f(u)/u)}$. The lower value $c_L = 2 \sqrt{f'(0)}$ is that predicted
by the linear marginal stability speed selection mechanism. We derive a new
lower bound on the the speed of the selected front, this bound depends on $f$
and thus enables us to assess the extent to which the linear marginal selection
mechanism is valid.
