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Tr. Mat. Inst. Steklova, 2018, Volume 300, Pages 146–157 (Mi tm3854)  

Couette flow of a viscoelastic Maxwell-type medium with two relaxation times

V. Yu. Liapidevskiiab

a Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, pr. Lavrent'eva 15, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: A Couette flow of a viscoelastic medium is considered that is described by the Johnson–Segalman–Oldroyd model with two relaxation times. The development of singularities related to the appearance of internal discontinuities is studied both analytically and numerically within one-dimensional nonstationary hyperbolic models of viscoelastic Maxwell-type media. A numerical model for calculating nonstationary one-dimensional discontinuous solutions is constructed, discontinuous solutions are studied, and the hysteresis phenomenon, i.e., the dependence of the structure of a steady Couette flow on the prehistory of its formation, is analyzed.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00127
This work was supported by the Russian Foundation for Basic Research, project no. 16-01-00127.


DOI: https://doi.org/10.1134/S0371968518010119

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 300, 137–148

Bibliographic databases:

UDC: 532.135+532.137
Received: September 1, 2017

Citation: V. Yu. Liapidevskii, “Couette flow of a viscoelastic Maxwell-type medium with two relaxation times”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Tr. Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 146–157; Proc. Steklov Inst. Math., 300 (2018), 137–148

Citation in format AMSBIB
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\paper Couette flow of a~viscoelastic Maxwell-type medium with two relaxation times
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 300
\pages 146--157
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3854}
\crossref{https://doi.org/10.1134/S0371968518010119}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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