Pullback-attractors for the modified Kelvin-Voigt model
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 98-104.

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

We study the qualitative dynamics of weak solutions for the modified Kelvin-Voigt model based on the theory of pullback attractors of trajectory spaces. First, for the studied model, an auxiliary problem is considered, its solvability in the weak sense is proved, and solution estimates are established. Then, on the basis of the obtained estimates of the solutions, a family of trajectory spaces is determined and the existence of trajectory and minimal pullback-attractors of the considered trajectory spaces is proved.
Keywords: pullback-attractor, trajectory space, modified Kelvin-Voigt model, weak solution, existence theorem.
@article{IVM_2021_5_a11,
     author = {A. S. Ustiuzhaninova},
     title = {Pullback-attractors for the modified {Kelvin-Voigt} model},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {98--104},
     publisher = {mathdoc},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_5_a11/}
}
TY  - JOUR
AU  - A. S. Ustiuzhaninova
TI  - Pullback-attractors for the modified Kelvin-Voigt model
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 98
EP  - 104
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_5_a11/
LA  - ru
ID  - IVM_2021_5_a11
ER  - 
%0 Journal Article
%A A. S. Ustiuzhaninova
%T Pullback-attractors for the modified Kelvin-Voigt model
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 98-104
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_5_a11/
%G ru
%F IVM_2021_5_a11
A. S. Ustiuzhaninova. Pullback-attractors for the modified Kelvin-Voigt model. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 98-104. http://geodesic.mathdoc.fr/item/IVM_2021_5_a11/

[1] Carvalho A.N., Langa J.A., Robinson J.C., Attractors for infinite-dimensional non-autonomous dynamical systems, Appl. Math. Sci., 182, Springer-Verlag, New York, 2013 | DOI | MR | Zbl

[2] Vorotnikov D., “Asymptotic behaviour of the non-autonomous $3$D Navier-Stokes problem with coercive force”, J. Diff. Equat., 251:8 (2011), 2209–2225 | DOI | MR | Zbl

[3] Pavlovskii V.A., “K voprosu o teoreticheskom opisanii slabykh vodnykh rastvorov polimerov”, Dokl. AN SSSR, 200:4 (1971), 809–812

[4] Amfilokhiev V.B., Voitkunskii Ya.I., Mazaeva N.P., Khodorkovskii Ya.S., “Techeniya polimernykh rastvorov pri nalichii konvektivnykh uskorenii”, Tr. Leningradsk. korablestroitelnogo in-ta, 96 (1975), 3–9

[5] Amfilokhiev V.B., Pavlovskii V.A., “Eksperimentalnye dannye o laminarno-turbulentnom perekhode pri techenii polimernykh rastvorov v trubakh”, Tr. Leningradsk. korablestroitelnogo in-ta, 104 (1976), 3–5

[6] Oskolkov A.P., “K teorii nestatsionarnykh techenii zhidkostei Kelvina–Foigta”, Zap. nauchn. sem. LOMI, 115, 1982, 191–202

[7] Oskolkov A.P., “Nachalno-kraevye zadachi dlya uravnenii dvizheniya zhidkostei Kelvina–Foigta i zhidkostei Oldroita”, Tr. MIAN SSSR, 179, 1988, 126–164

[8] Zvyagin V.G., Turbin M.V., “Issledovanie nachalno-kraevykh zadach dlya matematicheskikh modelei dvizheniya zhidkostei Kelvina–Foigta”, Gidrodinamika, SMFN, 31, RUDN, M., 2009, 3–144

[9] Zvyagin V.G., Turbin M.V., Matematicheskie voprosy gidrodinamiki vyazkouprugikh sred, KRASAND (URSS), M., 2012

[10] Turbin M.V., Ustyuzhaninova A.S., “Teorema suschestvovaniya slabogo resheniya nachalno-kraevoi zadachi dlya sistemy uravnenii, opisyvayuschei dvizhenie slabykh vodnykh rastvorov polimerov”, Izv. vuzov. Matem., 8 (2019), 62–78 | Zbl