  We prove the existence of a traveling wave solution for a boundary reaction
diffusion equation when the reaction term is the combustion nonlinearity with
ignition temperature. A key role in the proof is plaid by an explicit formula
for traveling wave solutions of a free boundary problem obtained as singular
limit for the reaction-diffusion equation (the so-called high energy activation
energy limit). This explicit formula, which is interesting in itself, also
allows us to get an estimate on the decay at infinity of the traveling wave
(which turns out to be faster than the usual exponential decay).
