  We derive the precise limit of SHS in the high activation energy scaling
suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J.
Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit turns
out to be the Stefan problem for supercooled water with spatially inhomogeneous
coefficients. Although the present paper leaves open mathematical questions
concerning the convergence, our precise form of the limit problem suggest a
strikingly simple explanation for the numerically observed pulsating waves.
