Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Critical behavior of an ignition model in chemical combustion

Author: Peter J. Tonellato
Journal: Quart. Appl. Math. 49 (1991), 795-812
MSC: Primary 80A25
DOI: https://doi.org/10.1090/qam/1134754
MathSciNet review: MR1134754
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Abstract: A model for the hot slab ignition problem is analyzed to determine critical conditions. The system is said to be super-critical if the solution of the reduced perturbation problem blows up in small finite time or sub-critical if the blow up time is large. Comparison principles for integral equations are used to construct upper and lower solutions of the equation. All solutions depend on two parameters $ {\varepsilon ^{ - 1}}$, the Zeĺdovitch number and $ \lambda $, the scaled hot slab size. Upper and lower bounds on a 'critical' curve $ {\lambda _c}\left( \epsilon \right)$ in the $ \left( {\epsilon, \lambda } \right)$ plane, separating the super-critical from the sub-critical region, are derived based upon the lower and upper solution behavior. Numerical results confirm the parameter space analysis.

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DOI: https://doi.org/10.1090/qam/1134754
Article copyright: © Copyright 1991 American Mathematical Society

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