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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 hypersonic aircraft permeable surfaces effective heat protection mathematical modeling problems are considered. The statements of one- and two-dimensional inverse problems of heat and mass transfer are given. The computational experiments results on control (the blowing) restoration by heat and mass transfer parameters (local heat flow and local friction) are discussed.

- approximation statement
- computational experiments
- control
- heat and mass transfer
- hypersonic flows
- interpolation statement
- inverse problems
- laminar boundary layer

- 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 inverse problems of heat and mass transfer on hypersonic aircraft permeable surfaces, " (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. 39-44
- Bilchenko G. G., Bilchenko N. G. " The one-dimensional and two-dimensional inverse problems of heat and mass transfer on hypersonic aircraft permeable surfaces, " (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. 26-32
- Bilchenko G. G., Bilchenko N. G. " On the One-Dimensional and Two-Dimensional Inverse Problems of Heat and Mass Transfer on Hypersonic Aircraft Permeable Surfaces, " (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. 224-229
- 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 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
- Bilchenko G. G., Bilchenko N. G. " Comparative analysis of some special blowing laws application in problems of heat and mass transfer optimal control on hypersonic aircraft permeable perforated surfaces, " (in Russian), Proc. International Scientific and Technical Conf. " Actual Problems of Applied Mathematics, Computer Science and Mechanics", Voronezh, December 16-18, 2015, Voronezh: Publishing House " Scientific Research Publications", 2015, pp. 134-136
- Bilchenko G. G., Bilchenko N. G. " Comparative analysis of some special blowing laws application in problems of heat and mass transfer optimal control on hypersonic aircraft permeable porous surfaces, " (in Russian), Proc. International Scientific and Technical Conf. " Actual Problems of Applied Mathematics, Computer Science and Mechanics", Voronezh, December 16-18, 2015, Voronezh: Publishing House " Scientific Research Publications", 2015, pp. 137-139
- 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 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. " The classes of solutions of the problems of boundary layer optimal control on the permeable surfaces of hypersonic aircrafts, " (in Russian), Proc. International Conf. " Voronezh Winter Math. School of S. G. Krein-2016" ed. V. A. Kostin, Russia, Voronezh, 2016, " Nauchnaya kniga" Publishers, pp. 82-86
- Bilchenko G. G., Bilchenko N. G. " Inverse problems of heat and mass transfer on hypersonic aircraft permeable surfaces. II. On some computational experiments, " (in Russian), Proceedings of Voronezh State University. Series: System Analysis and Information Technologies, 2016, no. 4, pp. 13-19
- Bilchenko G. G., Bilchenko N. G. " On some Computational Experiments in 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. 70-75
- 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 G. G., Bilchenko N. G. " Bijectivity of Controls Pairs and Pairs of Heat and Mass Transfer Local Parameters in the Hypersonic Flow Stagnation Point, " (in Russian), Differential Equations and Control Processes, 2017, no. 3, pp. 163-175. [ http://www.math.spbu.ru/diffjournal/ ]