Wave propagation in a qualitative model of combustion under equilibrium conditions
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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F. A. Williams, Combustion Theory, 2nd ed., Benjamin-Cummings, New York, 1985
G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable, McGraw-Hill, New York, 1966
B.-T. Chu, Wave propagation in a reacting mixture, 1958 Heat Transfer and Fluid Mechanics Institute, University of California-Berkeley, Stanford Univ. Press, 1958
W. Fickett, Detonation in miniature, Amer. J. Phys. 47 (12), 1050–1059 (1979)
W. Fickett, Introduction to Detonation Theory, Univ. of California Press, Berkeley, 1985
W. Fickett, Shock initiation of a dilute explosive, Phys. Fluids 27 (1), 94–105 (1984)
W. Fickett, Stability of the square-wave detonation in a model system, Phys. D 16, 358–370 (1985)
W. Fickett, Decay of small planar perturbations on a strong steady detonation, Phys. Fluids 30 (5), 1299–1309 (1987)
W. Fickett, A mathematical problem from detonation theory, Quart. Appl. Math. 46 (3), 459–471 (1987)
J. D. Logan, Applied Mathematics: A Contemporary Approach, Wiley-Interscience, New York, 1987
J. D. Logan and A. K. Kapila, Hydrodynamic stability of chemical equilibrium, Internat. J. Engrg. Sci. 27 (12), 1651–1659 (1989)
A. Majda, A qualitative model for dynamic combustion, SIAM J. Appl. Math. 41 (1), 70–93 (1981)
A. Majda, High mach number combustion, Reacting Flows, Lectures in Appl. Math., Vol. 24, Amer. Math. Soc., Providence, RI, 1986, pp. 109–184
W. G. Vincenti and C. H. Kruger. Introduction to Physical Gas Dynamics, Wiley, New York, 1965
G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974
F. A. Williams, Combustion Theory, 2nd ed., Benjamin-Cummings, New York, 1985
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Article copyright:
© Copyright 1991
American Mathematical Society