|
Asymptotic behavior of solutions of a complete second-order integro-differential equation
D. A. Zakora Vernadsky Crimean Federal University, Simferopol', Russia
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.
Citation:
D. A. Zakora, “Asymptotic behavior of solutions of a complete second-order integro-differential equation”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 68, no. 3, PFUR, M., 2022, 451–466
Linking options:
https://www.mathnet.ru/eng/cmfd468 https://www.mathnet.ru/eng/cmfd/v68/i3/p451
|
Statistics & downloads: |
Abstract page: | 123 | Full-text PDF : | 88 | References: | 18 |
|