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Sibirsk. Mat. Zh., 2018, Volume 59, Number 6, Pages 1351–1369 (Mi smj3048)  

On solvability of an initial-boundary value problem for a viscoelasticity model with fractional derivatives

V. G. Zvyagin, V. P. Orlov

Research Institute of Mathematics, Voronezh State University, Voronezh, Russia

Abstract: We establish the existence and uniqueness (the latter only in the plane case) of a weak solution to an initial-boundary value problem for the system of the equations of motion of a viscoelastic fluid, namely, for the anti-Zener model whose constitutive law contains fractional derivatives. We use the approximation of this problem by a sequence of regularized Navier–Stokes systems and passage to the limit.

Keywords: viscoelastic medium, equation of motion, initial-boundary value problem, weak solution, anti-Zener model, fractional derivative.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0037
The authors are supported by the Ministry of Education and Science of the Russian Federation (Grant 14.Z50.31.0037).


DOI: https://doi.org/10.17377/smzh.2018.59.610

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English version:
Siberian Mathematical Journal, 2018, 59:6, 1073–1089

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 27.01.2018

Citation: V. G. Zvyagin, V. P. Orlov, “On solvability of an initial-boundary value problem for a viscoelasticity model with fractional derivatives”, Sibirsk. Mat. Zh., 59:6 (2018), 1351–1369; Siberian Math. J., 59:6 (2018), 1073–1089

Citation in format AMSBIB
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\by V.~G.~Zvyagin, V.~P.~Orlov
\paper On solvability of an initial-boundary value problem for a~viscoelasticity model with fractional derivatives
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 6
\pages 1351--1369
\mathnet{http://mi.mathnet.ru/smj3048}
\crossref{https://doi.org/10.17377/smzh.2018.59.610}
\transl
\jour Siberian Math. J.
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\vol 59
\issue 6
\pages 1073--1089
\crossref{https://doi.org/10.1134/S0037446618060101}
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