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The Avalos–Triggiani Problem for the Linear Oskolkov System and a System of Wave Equations

Abstract

The Avalos–Triggiani problem for a system of wave equations and the linear Oskolkov system is investigated. The method proposed by G. Avalos and R. Triggiani is used to prove a theorem on the existence of a unique solution to the Avalos–Triggiani problem. The underlying mathematical model involves the linear Oskolkov system describing the flow of an incompressible viscoelastic Kelvin–Voigt fluid of zero order and a vector wave equation describing a structure immersed in the fluid.

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Funding

This work was supported in part by the Ministry of Science and Higher Education of the Russian Federation, grant no. FENU-2020-0022 (2020072GZ).

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Correspondence to G. A. Sviridyuk or T. G. Sukacheva.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Sviridyuk, G.A., Sukacheva, T.G. The Avalos–Triggiani Problem for the Linear Oskolkov System and a System of Wave Equations. Comput. Math. and Math. Phys. 62, 427–431 (2022). https://doi.org/10.1134/S0965542522020105

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  • DOI: https://doi.org/10.1134/S0965542522020105

Keywords:

  • Avalos–Triggiani problem
  • incompressible viscoelastic fluid
  • linear Oskolkov system