**
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE **

Vol. LXXVI, 1 (2007)

p. 99 - 109

Self-propagating High Temperature Synthesis (SHS) in the
High Activation Energy Regime

G. S. Weiss

**Abstract**.
We derive the precise limit of SHS in the high
activation energy scaling suggested by B. J. Matkowsky and G. I. Sivashinsky
in 1978 and by
A. Bayliss, B. J. Matkowsky and 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 suggests a strikingly simple explanation
for the numerically observed pulsating waves.

**Keywords.**
SHS, solid combustion, singular limit,
high activation energy, Stefan problem, ill-posed problem, free boundary, hysteresis.

**AMS Subject classification.** 80A25, 80A22, 35K55, 35R35.

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