On stabilization of solutions of integrodifferential incomplete second-order equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 78-83.

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We consider abstract linear integrodifferential incomplete second-order equations in the Hilbert space. Operator coefficients of these equations are unbounded selfadjoint nonnegative operators. These equations arise naturally in the study of problems of viscoelasticity and hydroelasticity. We prove a theorem on asymptotic stability of strong solutions of these equations.
Keywords: integrodifferential equation, stability.
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D. A. Zakora. On stabilization of solutions of integrodifferential incomplete second-order equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2016), pp. 78-83. http://geodesic.mathdoc.fr/item/IVM_2016_9_a8/

[1] Ilyushin A. A., Pobedrya B. E., Osnovy matematicheskoi teorii termovyazko-uprugosti, Nauka, M., 1970 | MR

[2] Prüss J., Evolutionary integral equations and applications, Monographs in Mathematics Series, 87, Birkhäuser Verlag, Basel, 1993 | DOI | MR | Zbl

[3] Kopachevsky N. D., Krein S. G., Operator approach to linear problems of hydrodynamics, v. 2, Nonself-adjoint problems for viscous fluids, Birkhäuser Verlag, Basel–Boston–Berlin, 2003 | MR | Zbl

[4] Zakora D., “A symmetric model of ideal rotating relaxing fluid”, J. Math. Sci., 7:2 (2011), 91–112 | MR

[5] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

[6] Pazy A., Semigroups of linear operators and applications to partial differential equations, Appl. Math. Sci., 44, Springer-Verlag, New York–Berlin, 1983 | DOI | MR | Zbl

[7] Gearhart L., “Spectral theory for contraction semigroups on Hilbert spaces”, Trans. Amer. Math. Soc., 236 (1978), 385–394 | DOI | MR | Zbl

[8] Engel K.-J., Nagel R., One-parameter semigroups for linear evolution equations, Springer-Verlag, Berlin–Heildelberg–New York, 2000 | MR | Zbl

[9] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR