Geodesic
Existence of the First Integral in a Problem of Optimally-Controlled BL Theory
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 150 (2008) no. 3, pp. 117-121 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper states the problem of minimizing the integral drag of friction in the presence of restrictions preset on the control system power. As the control, a specific flow rate of liquid is used here, injected into the basic flow through the porous or perforated section of the surface streamlined. This problem can be related to the class of Meyer's variation problems with two independent variables. It is significant here that the corresponding conservation law for conjugate system of equations transforms automatically into the first integral to be valid at any velocity on the outer BL border and at any Prandtl numbers chosen.
Keywords: boundary layer, optimal control, Noether's theory, Lie group theory. 
@article{UZKU_2008_150_3_a11,
     author = {K. G. Garaev},
     title = {Existence of the {First} {Integral} in {a~Problem} of {Optimally-Controlled} {BL} {Theory}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {117--121},
     year = {2008},
     volume = {150},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2008_150_3_a11/}
}
TY  - JOUR
AU  - K. G. Garaev
TI  - Existence of the First Integral in a Problem of Optimally-Controlled BL Theory
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2008
SP  - 117
EP  - 121
VL  - 150
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZKU_2008_150_3_a11/
LA  - ru
ID  - UZKU_2008_150_3_a11
ER  - 
%0 Journal Article
%A K. G. Garaev
%T Existence of the First Integral in a Problem of Optimally-Controlled BL Theory
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2008
%P 117-121
%V 150
%N 3
%U http://geodesic.mathdoc.fr/item/UZKU_2008_150_3_a11/
%G ru
%F UZKU_2008_150_3_a11
K. G. Garaev. Existence of the First Integral in a Problem of Optimally-Controlled BL Theory. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 150 (2008) no. 3, pp. 117-121. http://geodesic.mathdoc.fr/item/UZKU_2008_150_3_a11/

[1] Sirazetdinov T. K., “Optimalnye zadachi gazodinamiki”, Izv. vuzov. Aviatsionnaya tekhnika, 1963, no. 2, 11–21 | MR

[2] Garaev K. G., “Ob invariantnykh variatsionnykh zadachakh”, Tr. 1-i Povolzhsk. konf. “Avtomaticheskoe upravlenie”, Tatknigoizdat, Kazan, 1971, 121–129

[3] Sebisi T., Bredshou P., Konvektivnyi teploobmen, Mir, M., 1987, 590 pp.

[4] Garaev K. G., “Ob odnom sledstvii iz teoremy Neter dlya dvumernykh variatsionnykh zadach tipa Maiera”, Prikladnaya matematika i mekhanika, 44:3 (1980), 448–453 | MR | Zbl

[5] Miele A., “Obobschenie variatsionnoi zadachi na neskolko funktsii dvukh nezavisimykh peremennykh”, Teoriya optimalnykh aerodinamicheskikh form, Mir, M., 1969

[6] Belov S. V., Poristye materialy v mashinostroenii, Mashinostroenie, M., 1981, 247 pp.

[7] Ibragimov N. Kh., “Invariantnye variatsionnye zadachi i ikh zakony sokhraneniya”, Teoret. i matem. fizika, 1:3 (1960), 350–359

[8] Garaev K. G., Teoriya invariantnykh variatsionnykh zadach v probleme optimalnogo upravleniya, Izd-vo Kazan. tekhn. un-ta, Kazan, 2005, 150 pp.