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**Stability of a detonation wave.**
*(English)*
Zbl 0631.76070

We derive and analyze a generalization of the square-wave model for detonation. In the square-wave model, it is assumed that each particle reacts instantaneously, after a state-dependent induction time. All of the heat release takes place in an instantaneous reaction, and absolutely no heat is released in the induction zone. In the generalization of the square-wave model, it is not assumed that all of the heat is released instantaneously, but is released gradually. From this generalized model, we are able to recover the square-wave model by performing an appropriate limiting process. The most important result coming from this generalized model is the existence of a definite value of a parameter, which determines a stability boundary.

### MSC:

76L05 | Shock waves and blast waves in fluid mechanics |

80A25 | Combustion |

76E30 | Nonlinear effects in hydrodynamic stability |

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\textit{F. S. Hall} and \textit{G. S. S. Ludford}, Physica D 28, 1--17 (1987; Zbl 0631.76070)

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### References:

[1] | Fickett, W., Stability of the square-wave detonation in a model system, Physica, 16D, 358-370 (1985) · Zbl 0577.76065 |

[2] | Fickett, W., Detonation in Miniature, Amer. J. Physics, 47, 1050-1059 (1979) |

[3] | Tricomi, F. G., Integral Equations (1985), Dover: Dover New York |

[4] | Rosales, R. R.; Majda, A., Weakly Nonlinear Detonation Waves, ((1983), SIAM: SIAM Philadelphia), 1086-1118 · Zbl 0572.76062 |

[5] | Hall, F. S., Solidification in a Rotating Magnetic Field and Stability of a Detonation Wave, (Ph.D. Thesis (January 1987), Cornell University: Cornell University Ithaca, New York) |

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