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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 4, Pages 899–912
DOI: https://doi.org/10.17377/smzh.2016.57.412 (Mi smj2791) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Study of degenerate evolution equations with memory by operator semigroup methods

V. E. Fedorovab, L. V. Borela

a Chelyabinsk State University, Chelyabinsk, Russia
b South Ural State University, Chelyabinsk, Russia
Full-text PDF (338 kB) Citations (1)
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DOI: https://doi.org/10.17377/smzh.2016.57.412
Abstract: We reduce the problem with some history prescribed for an integrodifferential equation in a Banach space including memory effect to the Cauchy problem for some evolution system with a constant operator in a larger space that possesses a resolvent ($C_0$)-semigroup. This enables us to state conditions for the existence of a unique classical solution to the original problem. We use the results to study the unique solvability of problems with history prescribed for degenerate linear evolution equations with memory in Banach spaces. We show that the initial-boundary value problem for the linearized integrodifferential Oskolkov system describing the dynamics of Kelvin–Voigt fluids in linear approximation belongs to this class of problems.
Keywords: evolution equation, operator semigroup, equation with memory, integrodifferential equation, initial-boundary value problem, Kelvin–Voigt fluid.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0020
The authors were supported by the Laboratory of Quantum Topology of Chelyabinsk State University (Grant 14.Z50.31.0020 of the Government of the Russian Federation).
Received: 13.07.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 4, Pages 704–714
DOI: https://doi.org/10.1134/S0037446616040121
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. E. Fedorov, L. V. Borel, “Study of degenerate evolution equations with memory by operator semigroup methods”, Sibirsk. Mat. Zh., 57:4 (2016), 899–912; Siberian Math. J., 57:4 (2016), 704–714
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Сибирский математический журнал Siberian Mathematical Journal
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