Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About History Editorial Page Addresses Scope Editorial Staff Submission Review For Authors Publication Ethics Issues Русская версия

On the Conservation Laws in the Optimal Control Problem for Laminar Boundary Layer of Non-equilibrium Dissociating Gas

Author(s):

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.

bilchnat@gmail.com

Abstract:

The problems of mathematical modeling of optimal heat protection of permeable surfaces of hypersonic aircraft in non-equilibrium dissociating gas are considered. The group theory approach to the optimization of systems with distributed parameters is applied. Conservation laws on all operators of the group admissible by a system of nonlinear differential equations of parabolic type are constructed.

Keywords

References:

  1. Bilchenko N. G., Garaev K. G., Derbenev S. A. " On the problem of optimal control of electroconductive liquid laminar boundary layer in magnetic field, " Russian Aeronautics (Izvestiya VUZ Aviatsionnaya Tekhnika), 1994, Vol. 37, no. 1, pp. 23-27
  2. Bilchenko N. G., Garaev K. G. " On optimum control of laminar boundary layer of electroconductive gas by supersonic flow conditions, " Proceedings of 12th NATIONAL HEAT TRANSFER CONFERENCE (UIT), L'Aquila, Italy, 1994, pp. 213-224
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. Sirazetdinov T. K. " Optimization of Distributed Parameter Systems, " (in Russian). Nauka Publishers, Moscow, 1977, 478 p
  9. Bilchenko N. G., Garaev K. G. " On the existence of the first integral in an optimal problem with distributed parameters, " Russian Mathematics (Izvestiya VUZ. Matematika), 1993, Vol. 37, no. 12, pp. 30-33
  10. Garaev K. G. " On a corollary of the Noether theorem for the two-dimensional problem of the Mayer type, " Journal of Applied Mathematics and Mechanics, 1980, Vol. 44, no. 3, pp. 316-320
  11. Lie S., Scheffers G. " Vorlesungen ü ber Differentialgleichungen mit bekannten infinitesimalen Transformationsgruppen. " Leipzig, Teubner, 1891, 568 s
  12. Ovsyannikov L. V. " Group Analysis of Differential Equations. " Academic Press, N. Y., 1982, 416 p
  13. Noether E. " Invariante Variationsprobleme, " Nachrichten von der Kö niglichen Gesellschaft der Wissenschaften zu Gö ttingen, Mathematisch-Physikalische Klasse, Heft 2, 1918, ss. 235-257
  14. Garaev K. G. " Optimal control of heat and mass transfer in a laminar compressible-gas boundary layer on permeable surfaces, " Fluid Dynamics, 1988, Vol. 23, no. 3, pp. 399-406
  15. Bilchenko N. G., Ovchinnikov V. A. " On a Lie group that admits a nonlinear system of partial differential equations of parabolic type, " Russian Mathematics (Izvestiya VUZ. Matematika), 1997, Vol. 41, no. 1, pp. 66-71
  16. Bilchenko N. G. " On the Conservation Laws in the Problem of Electroconductive Gas Laminar Boundary Layer Optimal Control, " (in Russian), Differential Equations and Control Processes, 2018, no. 1, pp. 77-91. [ http://www.math.spbu.ru/diffjournal/ ]
  17. Bilchenko N. G., Garaev K. G., Ovchinnikov V. A. " Symmetry group and conservation laws in the problem of the optimal control of a laminar boundary layer of an unbalanced-dissociating gas, " Russian Mathematics (Izvestiya VUZ. Matematika), 1999, Vol. 43, no. 11, pp. 9-17
  18. Dorrance W. H. " Viscous hypersonic flow. " New York, McGraw-Hill, 1962, X + 334 p
  19. Belov S. V. " Porous metals in engineering. " (in Russian), [ Poristye metally v mashinostroenii ]. Moscow: Mashinostroenie, 1981, 247 p
  20. Dorodnitsyn A. A. " Laminar Boundary Layer, " (in Russian), [ Laminarnyj pogranichnyj sloj v szhimaemom gaze ]. Sb. Teoret. rabot po aerodinamike, Moscow: TsAGI, Oborongiz, 1957, pp. 140-173
  21. "Theory of optimum aerodynamic shapes", ed. by A. Miele. New York, London, Academic press, 1965, 478 p

Full text (pdf)