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 Sibirsk. Mat. Zh., 2014, Volume 55, Number 4, Pages 882–897 (Mi smj2579)

On a time nonlocal problem for inhomogeneous evolution equations

V. E. Fedorovab, N. D. Ivanovab, Yu. Yu. Fedorovac

a Laboratory of Quantum Topology, Chelyabinsk State University, Chelyabinsk, Russia
b South Ural State University, Chelyabinsk, Russia
c Chelyabinsk State University, Chelyabinsk, Russia

Abstract: Under consideration is some problem for inhomogeneous differential evolution equation in Banach space with an operator that generates a $C_0$-continuous semigroup and a nonlocal integral condition in the sense of Stieltjes. In case the operator has continuous inhomogeneity in the graph norm. We give the necessary and sufficient conditions for existence of a generalized solution for the problem of whether the nonlocal data belong to the generator domain. Estimates on solution stability are given, and some conditions are obtained for existence of the classical solution of the nonlocal problem. All results are extended to a Sobolev-type linear equation, the equation in Banach space with a degenerate operator at the derivative. The time nonlocal problem for the partial differential equation, modeling a filtrating liquid free surface, illustrates the general statements.

Keywords: nonlocal problem, operator semigroup, Sobolev-type equation, boundary value problem.

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English version:
Siberian Mathematical Journal, 2014, 55:4, 721–733

Bibliographic databases:

Document Type: Article
UDC: 517.9

Citation: V. E. Fedorov, N. D. Ivanova, Yu. Yu. Fedorova, “On a time nonlocal problem for inhomogeneous evolution equations”, Sibirsk. Mat. Zh., 55:4 (2014), 882–897; Siberian Math. J., 55:4 (2014), 721–733

Citation in format AMSBIB
\Bibitem{FedIvaFed14} \by V.~E.~Fedorov, N.~D.~Ivanova, Yu.~Yu.~Fedorova \paper On a~time nonlocal problem for inhomogeneous evolution equations \jour Sibirsk. Mat. Zh. \yr 2014 \vol 55 \issue 4 \pages 882--897 \mathnet{http://mi.mathnet.ru/smj2579} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3242603} \transl \jour Siberian Math. J. \yr 2014 \vol 55 \issue 4 \pages 721--733 \crossref{https://doi.org/10.1134/S0037446614040144} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000340941400014} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906509526} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. N. D. Ivanova, V. E. Fedorov, “Nelokalnaya po vremeni kraevaya zadacha dlya linearizovannoi sistemy uravnenii fazovogo polya”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:3 (2015), 10–15
2. A. I. Kozhanov, G. A. Lukina, “Nelokalnye zadachi s integralnym usloviem dlya differentsialnykh uravnenii nechetnogo poryadka”, Sib. elektron. matem. izv., 13 (2016), 452–466
3. A. A. Petrova, V. V. Smagin, “Convergence of the Galyorkin method of approximate solving of parabolic equation with weight integral condition on a solution”, Russian Math. (Iz. VUZ), 60:8 (2016), 42–51
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