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.

**[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

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