Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika"
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2021, Volume 13, Issue 2, Pages 5–10
DOI: https://doi.org/10.14529/mmph210201
(Mi vyurm475)
 

This article is cited in 7 scientific papers (total in 7 papers)

Mathematics

Invariant spaces of Oskolkov stochastic linear equations on the manifold

O. G. Kitaeva

South Ural State University, Chelyabinsk, Russian Federation
Full-text PDF (529 kB) Citations (7)
References:
Abstract: The Oskolkov equation is obtained from the Oskolkov system of equations describing the dynamics of a viscoelastic fluid, after stopping one of the spatial variables and introducing a stream function. The article considers a stochastic analogue of the linear Oskolkov equation for plane-parallel flows in spaces of differential forms defined on a smooth compact oriented manifold without boundary. In these Hilbert spaces, spaces of random K-variables and K-“noises” are constructed, and the question of the stability of solutions of the Oskolkov linear equation in the constructed spaces is solved in terms of stable and unstable invariant spaces and exponential dichotomies of solutions. Oskolkov stochastic linear equation is considered as a special case of a stochastic linear Sobolev-type equation, where the Nelson-Glicklich derivative is taken as the derivative, and a random process acts as the unknown. The existence of stable and unstable invariant spaces is shown for different values of the parameters entering into the Oskolkov equation.
Keywords: Sobolev-type equations, differential forms, Nelson-Glicklich derivative, invariant spaces.
Received: 16.01.2021
Document Type: Article
UDC: 517.9
Language: English
Citation: O. G. Kitaeva, “Invariant spaces of Oskolkov stochastic linear equations on the manifold”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 13:2 (2021), 5–10
Citation in format AMSBIB
\Bibitem{Kit21}
\by O.~G.~Kitaeva
\paper Invariant spaces of Oskolkov stochastic linear equations on the manifold
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2021
\vol 13
\issue 2
\pages 5--10
\mathnet{http://mi.mathnet.ru/vyurm475}
\crossref{https://doi.org/10.14529/mmph210201}
Linking options:
  • https://www.mathnet.ru/eng/vyurm475
  • https://www.mathnet.ru/eng/vyurm/v13/i2/p5
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024