Geodesic
A study of operator models arising in problems of hereditary mechanics
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 91-110
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We examine integro-differential equations with unbounded operator-valued coefficients. The principal part of such an equation is an abstract hyperbolic operator perturbed by Volterra integral operators whose kernels are fractional exponential functions of the type occurring in viscoelasticity. 
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V. V. Vlasov; N. A. Rautian. A study of operator models arising in problems of hereditary mechanics. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 32 (2019) no. 32, pp. 91-110. http://geodesic.mathdoc.fr/item/TSP_2019_32_32_a4/

[1] Rabotnov Yu. N., Elementy nasledstvennoi mekhaniki tverdykh tel, Nauka, M., 1977

[2] Ilyushin A. A., Pobedrya B. E., Osnovy matematicheskoi teorii termovyazkouprugosti, Nauka, M., 1970

[3] Gurtin M. E., Pipkin A. C., “General theory of heat conduction with finite wave speed”, Arch. Rat. Mech. Anal., 31 (1968), 113–126 | DOI | MR | Zbl

[4] Eremenko A., Ivanov S., “Spectra of the Gurtin-Pipkin Type Equations”, SIAM J. Math. Anal., 43:5 (2011), 2296–2306 | DOI | MR | Zbl

[5] Lykov A. V., Problema teplo- i massoobmena, Nauka i tekhnika, Minsk, 1976 | MR

[6] Vlasov V. V., Gavrikov A. A., Ivanov S. A., Knyaz'kov D. Yu., Samarin V. A., Shamaev A. S., “Spectral properties of combined media”, J. Math. Sci., 164:6 (2010), 948–963 | DOI | MR | Zbl

[7] Zhikov V. V., “Ob odnom rasshirenii i primenenii metoda dvukhmasshtabnoi skhodimosti”, Matem. sb., 191:7 (2000), 31–72 | DOI | MR | Zbl

[8] Vlasov V. V., Rautian N. A., “Korrektnaya razreshimost i spektralnyi analiz abstraktnykh giperbolicheskikh integrodifferentsialnykh uravnenii”, Tr. semin. im. I. G. Petrovskogo, 28, 2011, 75–114

[9] Vlasov V. V., Rautian N. A., Shamaev A. C., “Razreshimost i spektralnyi analiz integrodifferentsialnykh uravnenii, voznikayuschikh v teplofizike i akustike”, Dokl. RAN, 434:1 (2010), 12–15 | Zbl

[10] Vlasov V. V., Rautian N. A., Shamaev A. C., “Spektralnyi analiz i korrektnaya razreshimost abstraktnykh integrodifferentsialnykh uravnenii, voznikayuschikh v teplofizike i akustike”, SMFN, 39, 2011, 36–65

[11] Vlasov V. V., Rautian N. A., “Korrektnaya razreshimost i spektralnyi analiz integrodifferentsialnykh uravnenii, voznikayuschikh v teorii vyazkouprugosti”, SMFN, 58, 2015, 22–42

[12] Vlasov V. V., Rautian N. A., “Korrektnaya razreshimost volterrovykh integro-differentsialnykh uravnenii v gilbertovom prostranstve”, Tr. MMO, 75, no. 2, 2014, 131–155

[13] Vlasov V. V., Rautian N. A., Spektralnyi analiz funktsionalno-differentsialnykh uravnenii., MAKS Press, M., 2016

[14] Lions Zh. P., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, M., 1971

[15] Beitmen G., Erdeii A., Tablitsy integralnykh preobrazovanii. Preobrazovaniya Fure, Laplasa, Mellina, M., 1968

[16] Iosida K., Funktsionalnyi analiz, Mir, M., 1967

[17] Perez Ortiz R., Vlasov V. V., Rautian N. A., Spectral analysis of Volterra integrodifferential equations with the kernels, depending on parameter, 2017, arXiv: 1710.07112 [math.SP] | MR

[18] Sekefalvi-Nad B., Foyash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[19] Vlasov V. V., Perez Ortiz. R., Rautian N. A., “Study of Volterra integro-differential equations with kernels depending on a parameter”, Differ. Equ., 54:3 (2018), 363–380 | DOI | MR | Zbl

[20] Perez Ortiz R., Vlasov V. V., “Correct solvability of volterra integrodifferential equations in hilbert space”, Electron. J. Qualit. Theory Differ. Equ., 31 (2016), 1–17 | MR

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

[22] Skubachevskii A. L., “Ob odnom klasse funktsionalno-differentsialnykh operatorov, udovletvoryayuschikh gipoteze Kato”, Algebra i analiz, 30:2 (2018), 249–273