Loading [MathJax]/jax/output/CommonHTML/config.js
Prikladnaya Mekhanika i Tekhnicheskaya 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


Prikl. Mekh. Tekh. Fiz.:
Year:
Volume:
Issue:
Page:
Find




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

Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2018, Volume 59, Issue 6, Pages 39–51
DOI: https://doi.org/10.15372/PMTF20180604 (Mi pmtf499) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic formula for the spectrum of the linear problem describing periodic polymer flows in the infinite channel

A. M. Blokhinab, D. L. Tkachevab, A. V. Yegitovab

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
Full-text PDF (271 kB) Citations (7)
DOI: https://doi.org/10.15372/PMTF20180604
Abstract: A new rheological model (a modification of the Pokrovskii–Vinogradov model) is investigated. The model was shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with a complex geometry of the boundary. For the case where the main solution is an analogue of the Poiseuille flow in an infinite flat channel (viscoelastic polymer fluid considered), an asymptotic formula is obtained for the distribution of points of the spectrum of the linear problem. It is shown that small perturbations have the additional property of periodicity on the variable that runs along the axis of the channel.
Keywords: rheological model, polymer medium, flow type Poiseuille flows, Lyapunov stability.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00791а
Received: 20.10.2017
Revised: 05.03.2018
English version:
Journal of Applied Mechanics and Technical Physics, 2018, Volume 59, Issue 6, Pages 992–1003
DOI: https://doi.org/10.1134/S0021894418060044
Bibliographic databases:
Document Type: Article
UDC: 532.135, 517.956.6, 517.984.5
Language: Russian
Citation: A. M. Blokhin, D. L. Tkachev, A. V. Yegitov, “Asymptotic formula for the spectrum of the linear problem describing periodic polymer flows in the infinite channel”, Prikl. Mekh. Tekh. Fiz., 59:6 (2018), 39–51; J. Appl. Mech. Tech. Phys., 59:6 (2018), 992–1003
Citation in format AMSBIB
\Bibitem{BloTkaYeg18}
\by A.~M.~Blokhin, D.~L.~Tkachev, A.~V.~Yegitov
\paper Asymptotic formula for the spectrum of the linear problem describing periodic polymer flows in the infinite channel
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2018
\vol 59
\issue 6
\pages 39--51
\mathnet{http://mi.mathnet.ru/pmtf499}
\crossref{https://doi.org/10.15372/PMTF20180604}
\elib{https://elibrary.ru/item.asp?id=36517942}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2018
\vol 59
\issue 6
\pages 992--1003
\crossref{https://doi.org/10.1134/S0021894418060044}
Linking options:
  • https://www.mathnet.ru/eng/pmtf499
  • https://www.mathnet.ru/eng/pmtf/v59/i6/p39
    • This publication is cited in the following 7 articles:
    1. A. M. Blokhin, D. L. Tkachev, “Lyapunov instability of stationary flows of a polymeric fluid in a channel with perforated walls”, Sb. Math., 213:3 (2022), 283–299  mathnet  mathnet  crossref  crossref  isi  scopus
    2. A. M. Blokhin, D. L. Tkachev, “On Linearly Unstable Steady States of an MHD Model of an Incompressible Polymeric Fluid in the Case of Absolute Conductivity”, Sib. Adv. Math., 32:1 (2022), 1  crossref
    3. Alexander Blokhin, Dmitry Tkachev, INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2020), 2351, INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2020), 2021, 040057  crossref
    4. A. M. Blokhin, D. L. Tkachev, “MHD model of incompressible polymeric fluid. Linear instability of the resting state”, Complex Variables and Elliptic Equations, 66:6-7 (2021), 929  crossref
    5. A.M. Blokhin, D.L. Tkachev, “Stability of the Poiseuille-type flow for a MHD model of an incompressible polymeric fluid”, European Journal of Mechanics - B/Fluids, 80 (2020), 112  crossref
    6. Alexander Blokhin, Dmitry Tkachev, “MHD model of an incompressible polymeric fluid. Linear instability of the resting state”, J. Phys.: Conf. Ser., 1666:1 (2020), 012007  crossref
    7. A. M. Blokhin, D. L. Tkachev, “Stability of Poiseuille-type Flows for an MHD Model of an Incompressible Polymeric Fluid”, Fluid Dyn, 54:8 (2019), 1051  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
    Statistics & downloads:
    Abstract page:80
    Full-text PDF :19
     
      Contact us:
    math-net2025_05@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025