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Strong Solutions of One Model of Dynamics of Thermoviscoelasticity of a Continuous Medium with Memory

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Abstract

We study a system of equations of dynamics of a thermoviscoelastic continuous medium with an Oldroyd-type rheological relation, which generalizes a Navier–Stokes–Fourier system. In the planar case, we prove the unique existence of strong solutions. The proof is based on the construction of Galerkin approximations and their strong estimates, which provide the corresponding limit passage.

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Funding

This work was supported by the Russian Foundation for Basic Research, grant no. 20-01-00051.

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Authors and Affiliations

  1. Voronezh State University, 1 Universitetskaya pl., 394018, Voronezh, Russia

    V. G. Zvyagin & V. P. Orlov

Authors
  1. V. G. Zvyagin
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  2. V. P. Orlov
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Corresponding authors

Correspondence to V. G. Zvyagin or V. P. Orlov.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 6, pp. 95–101.

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Zvyagin, V.G., Orlov, V.P. Strong Solutions of One Model of Dynamics of Thermoviscoelasticity of a Continuous Medium with Memory. Russ Math. 65, 84–89 (2021). https://doi.org/10.3103/S1066369X21060098

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  • DOI: https://doi.org/10.3103/S1066369X21060098

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