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The operator approach to Il’yushin’s models of viscoelastic media under the isothermal processes of deformation

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Abstract

Three Il’yushin’s models of viscoelastic media are considered. The theorems of strong unique solvability of the corresponding initial boundary-value problems are proved. All models are uniformly reduced to the Cauchy problems for differential first-order equations in some Hilbert space under some restrictions on physical parameters. Using these equations, we pose the problems of a spectrum of various viscoelastic media.

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Authors and Affiliations

  1. V. I. Vernadskii Tavricheskii National University, 4, Vernadskii Prosp., Simferopol, 95007, Ukraine

    Dmitry A. Zakora

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  1. Dmitry A. Zakora
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Correspondence to Dmitry A. Zakora.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 10, No. 3, pp. 412–432, July–August, 2013.

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Zakora, D.A. The operator approach to Il’yushin’s models of viscoelastic media under the isothermal processes of deformation. J Math Sci 196, 705–720 (2014). https://doi.org/10.1007/s10958-014-1687-4

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  • DOI: https://doi.org/10.1007/s10958-014-1687-4

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