Optimal control in a~model of the motion of a~viscoelastic medium with objective derivative
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2009), pp. 55-61.

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

In this paper we consider the Jeffreys model of the motion of a viscoelastic incompressible medium with the Yaumann derivative. Within this model we study the optimal control problem for the right-hand sides of the initial boundary value problem. We prove the existence of the optimal strong solution.
Keywords: optimal control, viscoelastic incompressible medium, Jeffreys model, Yaumann derivative, topological degree.
@article{IVM_2009_5_a5,
     author = {V. G. Zvyagin and A. V. Kuznetsov},
     title = {Optimal control in a~model of the motion of a~viscoelastic medium with objective derivative},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--61},
     publisher = {mathdoc},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_5_a5/}
}
TY  - JOUR
AU  - V. G. Zvyagin
AU  - A. V. Kuznetsov
TI  - Optimal control in a~model of the motion of a~viscoelastic medium with objective derivative
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 55
EP  - 61
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_5_a5/
LA  - ru
ID  - IVM_2009_5_a5
ER  - 
%0 Journal Article
%A V. G. Zvyagin
%A A. V. Kuznetsov
%T Optimal control in a~model of the motion of a~viscoelastic medium with objective derivative
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 55-61
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_5_a5/
%G ru
%F IVM_2009_5_a5
V. G. Zvyagin; A. V. Kuznetsov. Optimal control in a~model of the motion of a~viscoelastic medium with objective derivative. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2009), pp. 55-61. http://geodesic.mathdoc.fr/item/IVM_2009_5_a5/

[1] Astarita Dzh., Marruchchi Dzh., Osnovy gidromekhaniki nenyutonovskikh zhidkostei, Mir, M., 1978, 312 pp.

[2] Fursikov A. V., “Zadachi upravleniya i teoremy, kasayuschiesya odnoznachnoi razreshimosti smeshannoi kraevoi zadachi dlya trekhmernykh uravnenii Nave–Stoksa i Eilera”, Matem. sb., 115(157):2 (1981), 281–306 | MR | Zbl

[3] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981, 408 pp. | MR | Zbl

[4] Gaevskii Kh., Grëger K., Zakharias K. M., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978, 336 pp. | MR

[5] Vorotnikov D. A., Zvyagin V. G., “On the existence of weak solutions for the initial-boundary value problem in the Jeffreys model of motion of a viscoelastic medium”, Abstr. Appl. Anal., 2004, no. 10, 815–829 | DOI | MR | Zbl

[6] Simon J., “Compact sets in the space $L_p(0,T;B)$”, Ann. Mat. Pura Appl. Ser. IV, 146 (1987), 65–96 | DOI | MR | Zbl

[7] Guilliope C., Saut J.-C., “Existence results for the flow of viscoelastic fluids with differential constitutive law”, Nonlinear Anal., 15:9 (1990), 849–869 | DOI | MR

[8] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969, 480 pp. | MR

[9] Ekland I., Temam R., Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979, 399 pp. | MR