Abstract
A supersonic flow in a channel of variable cross section is considered in a quasi-one-dimensional approximation in the framework of a model of infinitely thin detonation waves. An analytical method is developed using special coordinates to analyze the conditions for the existence of steady flow behind a detonation wave. On the basis of numerical experiments, it is shown that the detonation wave can be stabilized. A stability analysis of the steady state is performed with respect to small perturbations of heat release. This analysis allows one to make a selection of the emergent flow pattern.
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