Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] G. F. Carrier, M. Krook, and C. E. Pearson, Functions of a Complex Variable, McGraw-Hill, New York, 1966 MR 0222256
  • [2] B.-T. Chu, Wave propagation in a reacting mixture, 1958 Heat Transfer and Fluid Mechanics Institute, University of California-Berkeley, Stanford Univ. Press, 1958 MR 0098582
  • [3] W. Fickett, Detonation in miniature, Amer. J. Phys. 47 (12), 1050-1059 (1979)
  • [4] W. Fickett, Introduction to Detonation Theory, Univ. of California Press, Berkeley, 1985
  • [5] W. Fickett, Shock initiation of a dilute explosive, Phys. Fluids 27 (1), 94-105 (1984)
  • [6] W. Fickett, Stability of the square-wave detonation in a model system, Phys. D 16, 358-370 (1985) MR 805709
  • [7] W. Fickett, Decay of small planar perturbations on a strong steady detonation, Phys. Fluids 30 (5), 1299-1309 (1987)
  • [8] W. Fickett, A mathematical problem from detonation theory, Quart. Appl. Math. 46 (3), 459-471 (1987) MR 963582
  • [9] J. D. Logan, Applied Mathematics: A Contemporary Approach, Wiley-Interscience, New York, 1987 MR 907026
  • [10] J. D. Logan and A. K. Kapila, Hydrodynamic stability of chemical equilibrium, Internat. J. Engrg. Sci. 27 (12), 1651-1659 (1989) MR 1030402
  • [11] A. Majda, A qualitative model for dynamic combustion, SIAM J. Appl. Math. 41 (1), 70-93 (1981) MR 622874
  • [12] A. Majda, High mach number combustion, Reacting Flows, Lectures in Appl. Math., Vol. 24, Amer. Math. Soc., Providence, RI, 1986, pp. 109-184 MR 840071
  • [13] W. G. Vincenti and C. H. Kruger. Introduction to Physical Gas Dynamics, Wiley, New York, 1965
  • [14] G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York, 1974 MR 0483954
  • [15] F. A. Williams, Combustion Theory, 2nd ed., Benjamin-Cummings, New York, 1985

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 80A25, 76N15, 80A32

Retrieve articles in all journals with MSC: 80A25, 76N15, 80A32

Additional Information

DOI: https://doi.org/10.1090/qam/1121679
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society