The article demonstrates the tasks that require designing of shock-wave structure with extreme values of the total pressure recovery coefficient, the relationships between flow velocity, static pressure, temperatures, and acoustic constant of the medium - the acoustic impedance. The problem of designing optimal shock-wave structure for supersonic air intakes of external, internal and mixed compression. The transition from the study of shock-wave processes to managing them, as well as to the construction of shock-wave structures with desired properties is accompanied by the increasing complexity of the mathematical apparatus and numerical techniques. Long-term efforts in this area have allowed performing a parametric study of SWS with properties, extreme by some parameter. In terms of optimal control theory problems of SWP management are formulated. Optimal combination of shocks composed of oblique shocks of same direction and a closing straight shock. Another optimal combination can include oblique incident shock and one reflected from the wall and closing direct shock. The problem of designing optimal triple of configurations shock waves arises in the study of supersonic air. It intakes work at nonisobaric mode, flows in three-dimensional nozzles with nozzle shocks, detonation waves is discussed.
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