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In the class of optimal control problems for quantum systems, operator optimality conditions for control are constructed in the form of fixed-point problems in the control space. The equivalence of the obtained operator optimality conditions to the well-known Pontryagin maximum principle is shown. Based on the obtained operator forms of optimality conditions, new iterative methods for finding extreme equations satisfying the maximum principle are developed. A comparative analysis of the effectiveness of the proposed operator methods of the maximum principle with known methods is carried out on model examples of optimization of quantum systems.

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The temperature fields in two-layer plates under periodic temperature effects on one of the surfaces are considered. The transition to a steady-state temperature field is investigated. For numerical calculations, a program based on the implementation of the finite element method was used. The same steady-state periodic temperature field was obtained asymptotically and was compared with the results of a numerical experiment. Numerical tests showed that for loads close to explosion during detonation of gas mixtures in thermodynamic treatment measures, the periodic temperature field is established after 5-6 cycles of heat flow exposure. Also after analysis of temperature field in single-layer and double-layer plates it is shown that introduction of thermal protection allows to significantly lower temperature of surface under influence of heat flow.

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