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

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Author(s): R. Monneau | G. S. Weiss

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXVI;
Issue: 1;
Start page: 99;
Date: 2007;
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Keywords: SHS | solid combustion | singular limit | high activation energy | Stefan problem | ill-posed problem | free boundary | hysteresis

ABSTRACT
We derive the precise limit of SHS in the high activation energy scaling suggested by B. J. Matkowsky and G. I. Sivashinskyin 1978 and by A. Bayliss, B. J. Matkowsky and A. P. Aldushin in 2002. In the time-increasing case the limit turns out to bethe 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.
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