Geodesic
Asymptotic behavior of solutions of a complete second-order integro-differential equation
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 68 (2022) no. 3, pp. 451-466

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In this paper, we study a complete second-order integro-differential operator equation in a Hilbert space. The difference-type kernel of an integral perturbation is a holomorphic semigroup bordered by unbounded operators. The asymptotic behavior of solutions of this equation is studied. Asymptotic formulas for solutions are proved in the case when the right-hand side is close to an almost periodic function. The obtained formulas are applied to the study of the problem of forced longitudinal vibrations of a viscoelastic rod with Kelvin–Voigt friction. 
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     author = {D. A. Zakora},
     title = {Asymptotic behavior of solutions of a complete second-order integro-differential equation},
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     publisher = {mathdoc},
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     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2022_68_3_a3/}
}
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D. A. Zakora. Asymptotic behavior of solutions of a complete second-order integro-differential equation. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 68 (2022) no. 3, pp. 451-466. http://geodesic.mathdoc.fr/item/CMFD_2022_68_3_a3/