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 Mat. Zametki, 2019, Volume 105, Issue 6, Pages 839–856 (Mi mz11974)

Solvability of a Thermoviscoelastic Model of the Motion of Solutions of Polymers Satisfying the Objectivity Principle

A. V. Zvyagin

Voronezh State University

Abstract: The existence of weak solutions of the initial boundary-value problem for a mathematical model describing the motion of weakly concentrated aqueous solutions of polymers is proved. In the model under study, the rheological relation defining the type of the liquid satisfies the objectivity principle. To this end, a smoothed objective Jaumann derivative is considered in the rheological relation. Also, in the mathematical model, the viscosity of the medium depends on temperature, which leads to the appearance of an additional energy balance equation. The proof of the solvability of the problem under consideration is based on the approximation-topological approach to the study of hydrodynamic problems and on the theory of fractional powers of positive operators.

Keywords: existence theorem, weak solution, non-Newtonian medium, thermoviscoelasticity.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 14.Z50.31.0037 This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 14.Z50.31.0037).

DOI: https://doi.org/10.4213/mzm11974

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English version:
Mathematical Notes, 2019, 105:6, 831–845

Bibliographic databases:

UDC: 517.958
Revised: 18.04.2018

Citation: A. V. Zvyagin, “Solvability of a Thermoviscoelastic Model of the Motion of Solutions of Polymers Satisfying the Objectivity Principle”, Mat. Zametki, 105:6 (2019), 839–856; Math. Notes, 105:6 (2019), 831–845

Citation in format AMSBIB
\Bibitem{Zvy19} \by A.~V.~Zvyagin \paper Solvability of a Thermoviscoelastic Model of the Motion of Solutions of Polymers Satisfying the Objectivity Principle \jour Mat. Zametki \yr 2019 \vol 105 \issue 6 \pages 839--856 \mathnet{http://mi.mathnet.ru/mz11974} \crossref{https://doi.org/10.4213/mzm11974} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3954315} \elib{https://elibrary.ru/item.asp?id=37652169} \transl \jour Math. Notes \yr 2019 \vol 105 \issue 6 \pages 831--845 \crossref{https://doi.org/10.1134/S0001434619050213} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000473246800021} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85068181382} 

• http://mi.mathnet.ru/eng/mz11974
• https://doi.org/10.4213/mzm11974
• http://mi.mathnet.ru/eng/mz/v105/i6/p839

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V A. Zvyagin, “Navier-Stokes-alpha model with temperature-dependent viscosity”, Dokl. Math., 101:2 (2020), 122–125
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