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
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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},
publisher = {mathdoc},
volume = {150},
number = {3},
year = {2008},
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 PB - mathdoc 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 %I mathdoc %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/