Geodesic
Solvability of the Stationary Optimal Control Problem for Motion Equations of Second Grade Fluids
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 554-560.

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the optimal Dirichlet boundary control problem for stationary motion equations of second grade fluids. We consider boundary control of the flow on a bounded domain in $\mathbb{R}^n$, $n=2,3$. We show the existence of a weak solution minimizing a given cost functional.
Keywords: hydrodynamics, non-Newtonian fluids, second grade fluids, optimal control, Dirichlet boundary control. 
@article{SEMR_2012_9_a30,
     author = {E. S. Baranovskii},
     title = {Solvability of the {Stationary} {Optimal} {Control} {Problem} for {Motion} {Equations} of {Second} {Grade} {Fluids}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {554--560},
     publisher = {mathdoc},
     volume = {9},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2012_9_a30/}
}
TY  - JOUR
AU  - E. S. Baranovskii
TI  - Solvability of the Stationary Optimal Control Problem for Motion Equations of Second Grade Fluids
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2012
SP  - 554
EP  - 560
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2012_9_a30/
LA  - ru
ID  - SEMR_2012_9_a30
ER  - 
%0 Journal Article
%A E. S. Baranovskii
%T Solvability of the Stationary Optimal Control Problem for Motion Equations of Second Grade Fluids
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2012
%P 554-560
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2012_9_a30/
%G ru
%F SEMR_2012_9_a30
E. S. Baranovskii. Solvability of the Stationary Optimal Control Problem for Motion Equations of Second Grade Fluids. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 554-560. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a30/

[1] R. S. Rivlin, J. L. Ericksen, “Stress deformation relations for isotropic materials”, J. Rational Mech. Anal., 4 (1955), 322–425 | MR

[2] D. Cioranescu, E. H. Ouazar, “Existence and uniqueness for fluids of second grade”, Research Notes in Mathematics, 109, 1984, 308–340 | MR

[3] V. Coscia, G. P. Galdi, “Existence, uniqueness, and stability of regular steady motions of a second grade fluid”, Int. J. Non-Linear Mech., 29 (1994), 493–506 | DOI | MR | Zbl

[4] C. le Roux, “Existence and uniqueness of the flow of second-grade fluids with slip boundary conditions”, Arch. Rational Mech. Anal., 148 (1999), 309–356 | DOI | MR | Zbl

[5] R. V. Goldshtein, V. A. Gorodtsov, Mekhanika sploshnykh sred, v. I, Nauka. Fizmatlit, Moskva, 2000

[6] J. E. Dunn, R. L. Fosdick, “Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade”, Arch. Rational Mech. Anal., 56 (1974), 191–252 | DOI | MR | Zbl

[7] R. A. Adams, J. J. F. Fournier, Sobolev spaces, 2 ed., Elsevier, 2003 | MR

[8] A. V. Fursikov, Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999