Wave propagation in a qualitative model of combustion under equilibrium conditions

Logan, J. David

doi:10.1090/qam/1121679

Author: J. David Logan
Journal: Quart. Appl. Math. 49 (1991), 463-476
MSC: Primary 80A25; Secondary 76N15, 80A32
DOI: https://doi.org/10.1090/qam/1121679
MathSciNet review: MR1121679
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Abstract: We study various aspects of wave motion within the context of the Fickett-Majda qualitative model of combustion, under the assumption that the waves are propagating into an equilibrium state of a material governed by a two-way, model chemical reaction. In particular, we examine the hydrodynamic stability of an equilibrium state and the properties of a wavefront propagating into the state. We also investigate the signalling problem and use asymptotic methods and steepest descent to determine the long time behavior of the solution. Comparisons are made to the real physical model.

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