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 Mat. Sb., 1991, Volume 182, Number 10, Pages 1479–1512 (Mi msb1384)

This article is cited in 6 scientific papers (total in 6 papers)

On a problem with nonlocal boundary condition for a parabolic equation

L. A. Muravei, A. V. Filinovskii

Abstract: Well-posed solvability is proved in an appropriate energy space of a boundary value problem with a nonlocal boundary condition for a one-dimensional parabolic equation; two-sided uniform estimates of the solution are obtained, which replace the maximum principle. The existence of an optimal control of the diffusion coefficient in the problem of minimizing the quality functional is established in the class of functions of bounded variation.

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English version:
Mathematics of the USSR-Sbornik, 1993, 74:1, 219–249

Bibliographic databases:

UDC: 517.956.4
MSC: Primary 35K20, 35B45; Secondary 49J20
Received: 01.10.1990

Citation: L. A. Muravei, A. V. Filinovskii, “On a problem with nonlocal boundary condition for a parabolic equation”, Mat. Sb., 182:10 (1991), 1479–1512; Math. USSR-Sb., 74:1 (1993), 219–249

Citation in format AMSBIB
\Bibitem{MurFil91} \by L.~A.~Muravei, A.~V.~Filinovskii \paper On a~problem with nonlocal boundary condition for a~parabolic equation \jour Mat. Sb. \yr 1991 \vol 182 \issue 10 \pages 1479--1512 \mathnet{http://mi.mathnet.ru/msb1384} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1135936} \zmath{https://zbmath.org/?q=an:0774.35031|0765.35022} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993SbMat..74..219M} \transl \jour Math. USSR-Sb. \yr 1993 \vol 74 \issue 1 \pages 219--249 \crossref{https://doi.org/10.1070/SM1993v074n01ABEH003345} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993KQ22500016} 

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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. L. A. Muravei, A. V. Filinovskii, “On the non-local boundary-value problem for a parabolic equation”, Math. Notes, 54:4 (1993), 1045–1057
2. Yuandi Wang, “Weak solutions for nonlocal boundary value problems with low regularity data”, Nonlinear Analysis: Theory, Methods & Applications, 67:1 (2007), 103
3. Yuandi Wang, Shengzhou Zheng, “The Existence and Behavior of Solutions for Nonlocal Boundary Problems”, Bound Value Probl, 2009 (2009), 1
4. Fatma Kanca, Mansur I. Ismailov, “The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data”, Inverse Problems in Science and Engineering, 2011, 1
5. Pulkina L.S., “A nonlocal problem with integral conditions for hyperbolic equation”, Nanosistemy: fizika, khimiya, matematika, 2:4 (2011), 61–70
6. M.S.. Hussein, Daniel Lesnic, M.I.. Ismailov, “An inverse problem of finding the time-dependent diffusion coefficient from an integral condition”, Math. Meth. Appl. Sci, 2015, n/a
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