Abstract:
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.
The authors were supported by the Russian Foundation for Basic Research (project
no. 20-01-00051) and the Ministry of Education and Science of Russia (project
no. FZGU-2020-0035).
Citation:
A. S. Ustiuzhaninova, M. V. Turbin, “Trajectory and global attractors for a modified Kelvin—Voigt model”, Sib. Zh. Ind. Mat., 24:1 (2021), 126–138; J. Appl. Industr. Math., 15:1 (2021), 158–168
\Bibitem{UstTur21}
\by A.~S.~Ustiuzhaninova, M.~V.~Turbin
\paper Trajectory and global attractors for a modified Kelvin---Voigt model
\jour Sib. Zh. Ind. Mat.
\yr 2021
\vol 24
\issue 1
\pages 126--138
\mathnet{http://mi.mathnet.ru/sjim1125}
\crossref{https://doi.org/10.33048/SIBJIM.2021.24.110}
\elib{https://elibrary.ru/item.asp?id=46091818}
\transl
\jour J. Appl. Industr. Math.
\yr 2021
\vol 15
\issue 1
\pages 158--168
\crossref{https://doi.org/10.1134/S1990478921010142}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85104779407}
Linking options:
https://www.mathnet.ru/eng/sjim1125
https://www.mathnet.ru/eng/sjim/v24/i1/p126
This publication is cited in the following 10 articles:
Mikhail Turbin, Anastasiia Ustiuzhaninova, “Trajectory and Global Attractors for the Kelvin–Voigt Model Taking into Account Memory along Fluid Trajectories”, Mathematics, 12:2 (2024), 266
M. V. Turbin, A. S. Ustiuzhaninova, “Solvability of an Initial–Boundary Value Problem
for the Modified Kelvin–Voigt Model with Memory
along Fluid Motion Trajectories”, Diff Equat, 60:2 (2024), 180
A. S. Ustyuzhaninova, “Ravnomernye attraktory modeli Bingama”, Izv. vuzov. Matem., 2024, no. 8, 65–80
A. S. Ustiuzhaninova, “Uniform Attractors for the Bingham Model”, Russ Math., 68:8 (2024), 56
Victor Zvyagin, Mikhail Turbin, “Weak solvability of the initial-boundary value problem for a finite-order model of the inhomogeneous incompressible Kelvin-Voigt fluid without a positive lower bound on the initial condition of fluid density”, EECT, 2024
Victor Zvyagin, Mikhail Turbin, “Weak solvability of the initial-boundary value problem for inhomogeneous incompressible Kelvin–Voigt fluid motion model of arbitrary finite order”, J. Fixed Point Theory Appl., 25:3 (2023)
V. G. Zvyagin, A. S. Ustiuzhaninova, “Pullback Attractors of the Bingham Model”, Diff Equat, 59:3 (2023), 377
Mikhail Turbin, Anastasiia Ustiuzhaninova, “Pullback attractors for weak solution to modified Kelvin-Voigt model”, EECT, 11:6 (2022), 2055
M. V. Turbin, A. S. Ustiuzhaninova, “Convergence of attractors for an approximation to attractors of a modified Kelvin–Voigt model”, Comput. Math. Math. Phys., 62:2 (2022), 325–335
Ustiuzhaninova A.S., “Uniform Attractors For the Modified Kelvin-Voigt Model”, Differ. Equ., 57:9 (2021), 1165–1176
Citation in format AMSBIB
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