Abstract linear Volterra second-order integro-differential equations
Eurasian mathematical journal, Tome 7 (2016) no. 2, pp. 75-91.

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We study a class of time-dependent linear second-order integro-differential equations with the evolution equation approach. These equations arise naturally in the study of viscoelasticity. Existence theorems for strong solutions for three classes of complete integrodifferential second-order equations are obtained.
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D. A. Zakora. Abstract linear Volterra second-order integro-differential equations. Eurasian mathematical journal, Tome 7 (2016) no. 2, pp. 75-91. http://geodesic.mathdoc.fr/item/EMJ_2016_7_2_a5/

[1] G. Chen, R. Grimmer, “Integral equations as evolution equations”, Journal of Differential Equations, 45 (1982), 53–74 | DOI | MR | Zbl

[2] W. Desch, W. Schappacher, “Some perturbation results for analytic semigroups”, Math. Ann., 281 (1988), 157–162 | DOI | MR | Zbl

[3] K.-J. Engel, R. Nagel, One-parameter semigroups for linear evolution eqations, Graduate Texts in Math., 194, Springer-Verlag, 2000 | MR

[4] J. A. Goldstein, Semigroups of linear operators and applications, Vysha shkola, Kiev, 1989 (in Russian) | MR

[5] R. C. Grimmer, “Resolvent operators for integral equations in Banach space”, Transactions of the AMS, 273:4 (1982), 333–349 | DOI | MR | Zbl

[6] M. L. Heard, “An abstract semilinear hyperbolic Volterra integro-differential equation”, Journal of Mathematical Analysis and Applications, 80 (1981), 175–202 | DOI | MR | Zbl

[7] A. A. Ilushin, B. E. Pobedria, Mathematical theory of thermoviscoelasticity, Nauka, M., 1970 (in Russian)

[8] T. Kato, Perturbation theory for linear operators, Mir, M., 1972 (in Russian) | MR | Zbl

[9] N. D. Kopachevsky, E. V. Syomkina, “Linear Volterra integro-differential second-order equations unresolved with respect to the highestderivative”, Eurasian Mathematical Journal, 4:4 (2013), 64–87 | MR | Zbl

[10] S. G. Krein, Linear differential equations in Banach space, Nauka, M., 1967 (in Russian) | MR

[11] A. Lunardi, “Regular solutions for time dependent abstract integro-differential equations with singular kernel”, Journal of Mathematical Analysis and Applications, 130 (1988), 1–21 | DOI | MR | Zbl

[12] J. Prüss, Evolutionary integral equations and applications, Monographs in Math., 87, Birkhäuser Verlag, 1993 | DOI | MR | Zbl

[13] H. Tanabe, Equations of evolution, Pitnam, London, 1979 | MR | Zbl

[14] V. V. Vlasov, D. A. Medvedev, N. A. Rautian, “Functional differential equations in Sobolev spaces and their spectrum analysis”, Sovremennye problemy matematiki i mehaniki. Mathematics, 8, no. 1, 2011 (in Russian)