Geodesic
Integrodifferential equations in viscoelasticity theory
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2012), pp. 56-60.

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We prove the correct solvability of the initial problems for integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Such equations occur in many problems of the theory of viscoelasticity with memory and the heat transfer theory.
Keywords: integrodifferential equations, operator functions, correct solvability. 
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V. V. Vlasov; N. A. Rautian. Integrodifferential equations in viscoelasticity theory. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2012), pp. 56-60. http://geodesic.mathdoc.fr/item/IVM_2012_6_a5/

[1] Griniv R. O., Shkalikov A. A., “O puchke operatorov, voznikayuschem v zadache o kolebaniyakh sterzhnya s vnutrennim treniem”, Matem. zametki, 56:2 (1994), 114–131 | MR | Zbl

[2] Miloslavskii A. I., Spektralnye svoistva operatornogo puchka, voznikayuschego v vyazkouprugosti, Dep. v Ukr. NIINTI 13.07.87, No 1229-UK87, Kharkov, 1987, 53 pp.

[3] Miloslavskii A. I., “Ob ustoichivosti nekotorykh klassov evolyutsionnykh uravnenii”, Sib. matem. zhurnal, 26 (1985), 118–132 | MR

[4] Miloslavskii A. I., “O spektre neustoichivosti operatornogo puchka”, Matem. zametki, 49:4 (1991), 88–94 | MR | Zbl

[5] Vlasov V. V., Rautian N. A., Shamaev A. S., “Razreshimost i spektralnyi analiz integro-differentsialnykh uravnenii, voznikayuschikh v teplofizike i akustike”, Dokl. RAN, 434:1 (2010), 12–15 | MR | Zbl

[6] Vlasov V. V., Rautian N. A., Shamaev A. S., “Spektralnyi analiz i korrektnaya razreshimost abstraktnykh integro-differentsialnykh uravnenii, voznikayuschikh v teplofizike i akustike”, Sovremen. matem. Fundamentalnye napravleniya, 39, 2011, 36-65 | MR

[7] Lions Zh. L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, M., 1971 | MR

[8] Vlasov V. V., “O razreshimosti i svoistvakh reshenii funktsionalno-differentsialnykh uravnenii v gilbertovom prostranstve”, Matem. sb., 186:8 (1995), 67–92 | MR | Zbl

[9] Vlasov V. V., Medvedev D. A., “Funktsionalno-differentsialnye uravneniya v prostranstvakh Soboleva i svyazannye s nimi voprosy spektralnoi teorii”, Sovremen. matem. Fundamentalnye napravleniya, 30, 2008, 3–173 | MR

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

[11] Pandolfi L., “The controllability of the Gurtin–Pipkin equations: a cosine operator approach”, Appl. Math. Optim., 52 (2005), 143–165 | DOI | MR | Zbl

[12] Ivanov S., Pandolfi L., “Heat equations with memory: lack of controllability to the rest”, J. Math. Anal. and Appl., 355 (2009), 1–11 | DOI | MR | Zbl

[13] Vlasov V. V., Vu Dzh., “Spektralnyi analiz i razreshimost abstraktnykh giperbolicheskikh uravnenii s posledeistviem”, Differents. uravneniya, 45:4 (2009), 524–533 | MR | Zbl