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

This article is cited in 1 scientific paper (total in 1 paper)

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
Received: 20.02.2018
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
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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  crossref  isi
  • Математические заметки Mathematical Notes
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