Trajectory and global attractors for a modified Kelvin---Voigt model
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 126-138.

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

We study the qualitative behavior of weak solutions to an autonomous modified Kelvin—Voigt model on the base of the theory of attractors for noninvariant trajectory spaces. For the model under consideration, we determine the trajectory space, introduce the notions of a trajectory attractor and a global attractor, and prove the existence of these attractors.
Keywords: trajectory attractor, global attractor, trajectory space, modified Kelvin—Voigt model, weak solution.
@article{SJIM_2021_24_1_a9,
     author = {A. S. Ustiuzhaninova and M. V. Turbin},
     title = {Trajectory and global attractors for a modified {Kelvin---Voigt} model},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {126--138},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a9/}
}
TY  - JOUR
AU  - A. S. Ustiuzhaninova
AU  - M. V. Turbin
TI  - Trajectory and global attractors for a modified Kelvin---Voigt model
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2021
SP  - 126
EP  - 138
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a9/
LA  - ru
ID  - SJIM_2021_24_1_a9
ER  - 
%0 Journal Article
%A A. S. Ustiuzhaninova
%A M. V. Turbin
%T Trajectory and global attractors for a modified Kelvin---Voigt model
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2021
%P 126-138
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a9/
%G ru
%F SJIM_2021_24_1_a9
A. S. Ustiuzhaninova; M. V. Turbin. Trajectory and global attractors for a modified Kelvin---Voigt model. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 126-138. http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a9/

[1] V. A. Pavlovskii, “To the question of theoretical description of weak aqueous solutions of polymers”, Dokl. Akad. Nauk SSSR, 200:4 (1971), 809–812 (in Russian)

[2] M. V. Turbin, A. S. Ustiuzhaninova, “The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions”, Russian Math., 63:8 (2019), 54–69 | DOI | DOI | Zbl

[3] P. I. Plotnikov, M. V. Turbin, A. S. Ustiuzhaninova, “Existence theorem for a weak solution of the optimal feedback control problem for the modified Kelvin-Voigt model of weakly concentrated aqueous polymer solutions”, Dokl. Math., 100:2 (2019), 433–435 | DOI | DOI | Zbl

[4] V. Zvyagin, D. Vorotnikov, Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodinamics, Walter de Gruyter, Berlin, 2008 | DOI | MR

[5] V. G. Zvyagin, S. K. Kondrat'ev, Attractors of the equations of models of motion of viscoelastic media, Izd-vo Voronezh. Gos. Univ., Voronezh, 2010 (in Russian)

[6] V. G. Zvyagin, M. V. Turbin, Mathematical problems of hydrodynamics of viscoelastic media, KRASAND, M., 2012 (in Russian)

[7] J. Simon, “Compact sets in the space $L^p (0, T; B)$”, Ann. Mat. Pur. Appl., 146 (1986), 65–96 | DOI | MR

[8] R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, North Holland, Amsterdam–N.Y.–Oxford, 1979 | MR | Zbl | Zbl

[9] V. G. Zvyagin, M. V. Turbin, “The study of initial-boundary value problems for mathematical models of the motion of Kelvin-Voigt fluids”, J. Math. Sci., 168 (2010), 157–308 | DOI | MR | Zbl