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**Grigorij Grigorievich Bilchenko**

Candidate of Science in Physics and Mathematics

Researcher of Research Laboratory #16,

Department of Heat Engineering and Power Engineering Machinery,

Kazan National Research Technical University (KNRTU-KAI)

named after A. N. Tupolev.

10, K. Marx St., Kazan, Tatarstan 420111, Russia

**Natalya Grigorievna Bilchenko**

Candidate of Science in Physics and Mathematics

Researcher of Research Laboratory #16,

Department of Heat Engineering and Power Engineering Machinery,

Kazan National Research Technical University (KNRTU-KAI)

named after A. N. Tupolev.

10, K. Marx St., Kazan, Tatarstan 420111, Russia

The conditions of heat and mass transfer local parameters and boundary layer parameters monotonous dependence on controls are given. The diffeomorphness conditions for controls pairs and pairs of heat and mass transfer local parameters are established. The computational experiments are presented. The domains of allowed values "heat-friction" are obtained.

- computational experiments
- control
- diffeomorphism
- heat and mass transfer
- hypersonic flows
- inverse problems
- laminar boundary layer
- stagnation point

- Bilchenko G. G., Bilchenko N. G. " On an inverse problem of heat and mass transfer, " (in Russian), Differential Equations and Control Processes, 2016, no. 2, Part 2, " Herzen Readings - 2016. Some Actual Probl. of Modern Math. and Math. Educ. " ed. V. F. Zaytsev, V. D. Budaev, A. V. Flegontov (Russia, Saint-Petersburg) pp. 50-56. [ http://www.math.spbu.ru/diffjournal/pdf/herzen2016.pdf ]
- Bilchenko G. G., Bilchenko N. G. " On the heat and mass transfer local parameters unique dependence on the controls at the hypersonic flow stagnation point, " (in Russian), Proc. International Conf. Voronezh Winter Math. School " Modern methods of function theory and related problems" (Russia, Voronezh, January 26 - February 1, 2017), Publishing House of VSU, 2017, pp. 44-48
- Bilchenko G. G., Bilchenko N. G. " On the diffeomorphness of controls pairs and pairs of heat and mass transfer local parameters in the hypersonic flow stagnation point, " (in Russian), Proc. Scientific Conf. " Herzen Readings - 2017. Some Actual Probl. of Modern Math. and Math. Educ. " ed. V. F. Zaytsev, V. D. Budaev, A. V. Flegontov (Russia, Saint-Petersburg, April 10-14, 2017), A. I. Herzen's RGPU Publishers, 2017, pp. 33-38
- Bilchenko G. G., Bilchenko N. G. " On the Bijectivity of Controls Pairs and Pairs of Heat and Mass Transfer Local Parameters in the Hypersonic Flow Stagnation Point, " (in Russian), Abstracts of the International Conference " Constructive Nonsmooth Analysis and Related Topics" Dedicated to the Memory of Professor V. F. Demyanov (Russia, Saint Petersburg, May 22-27, 2017), Saint Petersburg, VVM Publishing Lld., 2017, Part I, pp. 229-232
- Bilchenko G. G., Bilchenko N. G. " On the control synthesis in inverse problems of heat and mass transfer on the permeable surfaces of hypersonic aircrafts, " (in Russian), Proc. 11th International Chetaev Conference " Analytical Mechanics, Stability and Control" (Russia, Kazan, June 13-17, 2017), KNRTU-KAI Publishers, 2017, Vol. 3, Section 3 " Control", Part I, pp. 126-135
- Bilchenko G. G., Bilchenko N. G. " On the computational experiments of effective heat and mass transfer control synthesis in direct and inverse problems of hypersonic aerodynamics, " (in Russian), Proc. 11th International Chetaev Conference " Analytical Mechanics, Stability and Control" (Russia, Kazan, June 13-17, 2017), KNRTU-KAI Publishers, 2017, Vol. 3, Section 3 " Control", Part I, pp. 136-145
- Bilchenko G. G., Bilchenko N. G. " Inverse Problems of Heat and Mass Transfer on Hypersonic Aircraft Permeable Surfaces: One-Dimensional and Two-Dimensional Cases, " (in Russian), Differential Equations and Control Processes, 2017, no. 3, pp. 148-162. [ http://www.math.spbu.ru/diffjournal/ ]
- Bilchenko G. G., Bilchenko N. G. " On the boundary layer parameters unique dependence on the controls at the hypersonic flow stagnation point, " (in Russian), Proc. International Conf. " Modern methods of the boundary value problems theory" Voronezh Spring Math. School «Pontryagin Readings - XXVII» (Russia, Voronezh, May 3-9, 2016), Publishing House of VSU, 2016, pp. 46-48
- Bilchenko N. G. " Computational experiments in the problems of heat and mass transfer optimal control on permeable surfaces in electro-conductive gas laminar boundary layer, " (in Russian), Proceedings of Voronezh State University. Series: System Analysis and Information Technologies, 2016, no. 3, pp. 5-11
- Bilchenko G. G., Bilchenko N. G. " Inverse problems of heat and mass transfer on hypersonic aircraft permeable surfaces. I. Statements and possibility of control restoration, " (in Russian), Proceedings of Voronezh State University. Series: System Analysis and Information Technologies, 2016, no. 4, pp. 5-12
- Bilchenko G. G., Bilchenko N. G. " On the possibility of control restoration in some inverse problems of heat and mass transfer, " (in Russian), Proc. 11th International Conf. " Mesh Methods for Boundary-Value Problems and Applications - 2016" (Russia, Kazan, October 20-25, 2016), Kazan University Publishers, pp. 64-69
- Bilchenko N. G. " A. A. Dorodnitsyn's method in the problems of permeable surfaces in electroconductive gas laminar boundary layer heat and mass transfer optimal control, " (in Russian), Proceedings of Voronezh State University. Series: System Analysis and Information Technologies, 2016, no. 1, pp. 5-14
- Bilchenko G. G., Bilchenko N. G. " Inverse problems of heat and mass transfer on hypersonic aircrafts permeable surfaces. III. On the statement of two dimensional problems and the ranges of allowed values «heat - friction», " (in Russian), Proceedings of Voronezh State University. Series: System Analysis and Information Technologies, 2017, no. 1, pp. 18-25
- Bilchenko N. G. " Computation experiments in the problems of heat and mass transfer optimal control on permeable surfaces in hypersonic flows, " (in Russian), Proceedings of Voronezh State University. Series: Physics. Mathematics, 2015, no. 1, pp. 83-94
- Bilchenko N. G. " Computation experiments in the problems of heat and mass transfer optimal control on permeable spherical surfaces in hypersonic flows, " (in Russian), Proceedings of Voronezh State University. Series: System Analysis and Information Technologies, 2015, no. 1, pp. 5-8
- Bilchenko N. G. " Computation experiments in the problems of heat and mass transfer optimal control on permeable surfaces in hypersonic flows: comparative analysis of " simple" blow laws use, " (in Russian), Proceedings of Voronezh State University. Series: Physics. Mathematics, 2015, no. 1, pp. 95-102