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 , the Zeĺdovitch number and , the scaled hot slab size. Upper and lower bounds on a 'critical' curve in the 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