@article{TSP_2023_33_33_a4,
author = {V. V. Vlasov and N. A. Rautian},
title = {{\CYRI}{\cyrs}{\cyrs}{\cyrl}{\cyre}{\cyrd}{\cyro}{\cyrv}{\cyra}{\cyrn}{\cyri}{\cyre} {\cyrg}{\cyre}{\cyrn}{\cyre}{\cyrr}{\cyra}{\cyrt}{\cyro}{\cyrr}{\cyro}{\cyrv} {\cyrp}{\cyro}{\cyrl}{\cyru}{\cyrg}{\cyrr}{\cyru}{\cyrp}{\cyrp}, {\cyrp}{\cyro}{\cyrr}{\cyro}{\cyrzh}{\cyrd}{\cyra}{\cyre}{\cyrm}{\cyrery}{\cyrh} {\cyrv}{\cyro}{\cyrl}{\cyrsftsn}{\cyrt}{\cyre}{\cyrr}{\cyrr}{\cyro}{\cyrv}{\cyrery}{\cyrm}{\cyri} {\cyri}{\cyrn}{\cyrt}{\cyre}{\cyrg}{\cyrr}{\cyro}-{\cyrd}{\cyri}{\cyrf}{\cyrf}{\cyre}{\cyrr}{\cyre}{\cyrn}{\cyrc}{\cyri}{\cyra}{\cyrl}{\cyrsftsn}{\cyrn}{\cyrery}{\cyrm}{\cyri} {\cyru}{\cyrr}{\cyra}{\cyrv}{\cyrn}{\cyre}{\cyrn}{\cyri}{\cyrya}{\cyrm}{\cyri}},
journal = {Trudy Seminara im. I.G. Petrovskogo},
pages = {54--82},
year = {2023},
volume = {33},
number = {33},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TSP_2023_33_33_a4/}
}
TY - JOUR AU - V. V. Vlasov AU - N. A. Rautian TI - Исследование генераторов полугрупп, порождаемых вольтерровыми интегро-дифференциальными уравнениями JO - Trudy Seminara im. I.G. Petrovskogo PY - 2023 SP - 54 EP - 82 VL - 33 IS - 33 UR - http://geodesic.mathdoc.fr/item/TSP_2023_33_33_a4/ LA - ru ID - TSP_2023_33_33_a4 ER -
%0 Journal Article %A V. V. Vlasov %A N. A. Rautian %T Исследование генераторов полугрупп, порождаемых вольтерровыми интегро-дифференциальными уравнениями %J Trudy Seminara im. I.G. Petrovskogo %D 2023 %P 54-82 %V 33 %N 33 %U http://geodesic.mathdoc.fr/item/TSP_2023_33_33_a4/ %G ru %F TSP_2023_33_33_a4
V. V. Vlasov; N. A. Rautian. Исследование генераторов полугрупп, порождаемых вольтерровыми интегро-дифференциальными уравнениями. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 33 (2023) no. 33, pp. 54-82. http://geodesic.mathdoc.fr/item/TSP_2023_33_33_a4/
[1] Ilyushin A. A., Pobedrya B. E., Osnovy matematicheskoi teorii termovyazkouprugosti, Nauka, M., 1970 | MR
[2] Christensen R. M., Theory of viscoelasticity. An introduction, Academic Press, New York, 1971
[3] Rabotnov Yu. N., Elementy nasledstvennoi mekhaniki tverdykh tel, Nauka, M., 1977 | MR
[4] Munoz Rivera J. E., Naso M. G., Vegni F. M., “Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory”, J. Math. Anal. Appl., 286 (2003), 692–704 | DOI | MR | Zbl
[5] Kopachevsky N. D., Krein S. G., Operator Approach to Linear Problems of Hydrodynamics, v. 2, Operator Theory: Advances and Applications, 146, Nonself-Adjoint Problems for Viscous Fluids, Birkhäuser, Basel, 2003 | MR | Zbl
[6] Zakora D. A., “Asymptotics of Solutions in the Problem about Small Motions of a Compressible Maxwell Fluid”, Differ. Equ., 55:9 (2019), 1150–1163 | DOI | MR | Zbl
[7] Lokshin A. A., Suvorova Yu. V., Matematicheskaya teoriya rasprostraneniya voln v sredakh s pamyatyu, Izd-vo Mosk. un-ta, M., 1982
[8] Gurtin M. E., Pipkin A. C., “General theory of heat conduction with finite wave speed”, Arch. Ration. Mech. Anal., 31 (1968), 113–126 | DOI | MR | Zbl
[9] Lykov A. V., Problemy teplo- i massoperenosa, Minsk, 1976
[10] Amendola G., Fabrizio M., Golden J. M., Thermodynamics of Materials with Memory. Theory and Applications, Springer, Dordrecht, 2012 | MR | Zbl
[11] Miller R. K., “An integrodifferencial equation for rigid heat conductors with memory”, J. Math. Anal., 66 (1978), 313–332 | DOI | MR | Zbl
[12] Sanches-Palensiya E., Neodnorodnye sredy i teoriya kolebanii, Mir, M., 1984 | MR
[13] Vlasov V. V., Rautian N. A., Spektralnyi analiz funktsionalno-differentsialnykh uravnenii, MAKS Press, M., 2016
[14] Vlasov V. V., Rautian N. A., “Well-posedness and spectral analysis of integrodifferential equations arising in viscoelasticity theory”, J. Math. Sci., 233:4 (2018), 555–577 | DOI | MR | Zbl
[15] Vlasov V. V., Rautian N. A., “Spectral analysis of integrodifferential equations in Hilbert spaces”, J. Math. Sci, 239:5 (2019), 771–787 | DOI | MR | Zbl
[16] Vlasov V. V., Rautian N. A., “On Volterra integro-differential equations with kernels representable by Stieltjes integrals”, Differ. Equ, 57:4 (2021), 517–532 | DOI | MR | Zbl
[17] Rautian N. A., “Semigroups generated by Volterra integro-differential equations”, Differ. Equ, 56:9 (2020), 1193–1211 | DOI | MR | Zbl
[18] Rautian N. A., “On the properties of semigroups generated by Volterra integro-differential equations with kernels representable by Stieltjes integrals”, Differ. Equ., 57:9 (2021), 1255–1272 | DOI | MR | Zbl
[19] Eremenko A., Ivanov S., “Spectra of the Gurtin–Pipkin type equations”, SIAM J. Math. Anal, 43 (2011), 2296–2306 | DOI | MR | Zbl
[20] Dafermos C. M., “Asymptotic stability in viscoelasticity”, Arch. Ration. Mech. Anal., 37 (1970), 297–308 | DOI | MR | Zbl
[21] Engel K.-J., Nagel R., One-Parameter Semigroup for Linear Evolution Equations, Springer, 1999 | MR
[22] Pata V., “Stability and exponential stability in linear viscoelasticity”, Milan J. Math., 77 (2009), 333–360 | DOI | MR | Zbl
[23] Miloslavskii A. I., Spektralnye svoistva operatornogo puchka, voznikayuschego v vyazkouprugosti, Dep. v Ukr. NIINTI. 13.07.87. No 1229-UK87, Kharkov, 1987, 53 pp.
[24] Shkalikov A. A., “Silno dempfirovannye puchki operatorov i razreshimost sootvetstvuyuschikh operatorno-differentsialnykh uravnenii”, Mat. sb., 177:1 (1988), 96–118 | Zbl
[25] Smirnov V. I., Kurs vysshei matematiki, v. 5, Nauka, M., 1974 | MR
[26] Gelfand I. M., Vilenkin N. Ya., Nekotorye primeneniya garmonicheskogo analiza. Osnaschennye gilbertovy prostranstva, Fizmatgiz, M., 1961
[27] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967
[28] Gokhberg I. Ts., Krein S. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965
[29] Kato T., Perturbation theory for linear operators, Springer, 1966 | MR | Zbl