On the detonation of combustible gas. (English) Zbl 0543.76152
This paper is concerned with the existence of detonation waves for a combustible gas. The equations are those of a viscous, heat conducting, polytropic gas coupled with an additional equation which governs the evolution of the mass fraction of the unburned gas. The problem reduces to finding an orbit of an associated system of four ordinary differential equations which connects two distinct critical points. The proof employs topological methods, including C. Conley’s index of isolated invariant sets [Isolated invariant sets and the generalized Morse index (1978; Zbl 0397.34056)].
MSC:
| 76V05 | Reaction effects in flows |
| 80A25 | Combustion |
| 58J20 | Index theory and related fixed-point theorems on manifolds |
Keywords:
existence of detonation waves; combustible gas; viscous, heat conducting, polytropic gas; four ordinary differential equations; two distinct critical points; topological methods; C. Conley’s index of isolated invariant setsCitations:
Zbl 0397.34056References:
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