Journal of Applied Mechanics and Technical Physics

, Volume 59, Issue 6, pp 992–1003 | Cite as

Asymptotic Formula for the Spectrum of the Linear Problem Describing Periodic Polymer Flows in an Infinite Channel

  • A. M. BlokhinEmail author
  • D. L. Tkachev
  • A. V. Yegitov


In this paper, we study a new rheological model (a modification of the well-known Pokrovskii–Vinogradov model) which is shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with complex boundary geometry. 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 in the variable that runs along the axis of the channel.


rheological model polymer medium Poiseuille type flow Lyapunov stability 


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Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  • A. M. Blokhin
    • 1
    • 2
    Email author
  • D. L. Tkachev
    • 1
    • 2
  • A. V. Yegitov
    • 1
    • 2
  1. 1.Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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