### 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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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