Asymptotic Behavior of Solutions of a Complete Second-Order Integro-Differential Equation

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Abstract

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.

About the authors

D. A. Zakora

Vernadsky Crimean Federal University

Author for correspondence.
Email: dmitry.zkr@gmail.com
Simferopol’, Russia

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