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Plane waves and uniqueness theorems in the theory of viscoelastic mixtures

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Abstract

In the present paper, the linear theory of binary viscoelastic mixtures is considered. The basic properties of plane harmonic waves are established. Green’s first identity for 3D bounded and unbounded domains is obtained. On the basis of this identity the uniqueness theorems of regular (classical) solutions of the boundary value problems (BVPs) of steady vibrations are proved. Then these theorems are established in the quasi-static case. Finally, the uniqueness theorems for the first internal and external BVPs of steady vibrations in general and quasi-static cases are proved under weak condition on the viscoelastic constants.

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Authors and Affiliations

  1. Faculty of Exact and Natural Sciences, Tbilisi State University, I. Chavchavadze Ave., 3, 0179, Tbilisi, Georgia

    Maia M. Svanadze

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  1. Maia M. Svanadze
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Correspondence to Maia M. Svanadze.

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This research has been performed by financial support of Shota Rustaveli National Science Foundation (Grant #YS15_ 2.1.1_ 100).

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Svanadze, M.M. Plane waves and uniqueness theorems in the theory of viscoelastic mixtures. Acta Mech 228, 1835–1849 (2017). https://doi.org/10.1007/s00707-017-1799-2

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  • DOI: https://doi.org/10.1007/s00707-017-1799-2

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