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Mathematics of the USSR-Sbornik, 1993, Volume 74, Issue 1, Pages 219–249
DOI: https://doi.org/10.1070/SM1993v074n01ABEH003345 (Mi sm1384) 		 
This article is cited in 10 scientific papers (total in 10 papers)

On a problem with nonlocal boundary condition for a parabolic equation

L. A. Muravei, A. V. Filinovskii
English version PDF (1324 kB) Citations (10) Russian version article
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DOI: https://doi.org/10.1070/SM1993v074n01ABEH003345
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.
Received: 01.10.1990
Bibliographic databases:
UDC: 517.956.4
MSC: Primary 35K20, 35B45; Secondary 49J20
Language: English
Original paper language: Russian
Citation: L. A. Muravei, A. V. Filinovskii, “On a problem with nonlocal boundary condition for a parabolic equation”, Math. USSR-Sb., 74:1 (1993), 219–249
Citation in format AMSBIB
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\by L.~A.~Muravei, A.~V.~Filinovskii
\paper On a~problem with nonlocal boundary condition for a~parabolic equation
\jour Math. USSR-Sb.
\yr 1993
\vol 74
\issue 1
\pages 219--249
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    • This publication is cited in the following 10 articles:
    1. S. S. Weli, M. S. Hussein, 2ND INTERNATIONAL CONFERENCE FOR ENGINEERING SCIENCES AND INFORMATION TECHNOLOGY (ESIT 2022): ESIT2022 Conference Proceedings, 3009, 2ND INTERNATIONAL CONFERENCE FOR ENGINEERING SCIENCES AND INFORMATION TECHNOLOGY (ESIT 2022): ESIT2022 Conference Proceedings, 2024, 090006  crossref
    2. E. V. Tabarintseva, “O reshenii nelokalnoi obratnoi zadachi dlya parabolicheskogo uravneniya”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 16:2 (2024), 59–71  mathnet  crossref
    3. I. B. Garipov, R. M. Mavlyaviev, “Nelokalnaya zadacha s integralnym usloviem dlya parabolicheskogo uravneniya s operatorom Besselya”, Vestnik rossiiskikh universitetov. Matematika, 27:139 (2022), 231–246  mathnet  crossref
    4. Mansur I. Ismailov, Bülent Oğur, “An inverse diffusion problem with nonlocal boundary conditions”, Numerical Methods Partial, 32:2 (2016), 564  crossref
    5. 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  crossref  mathscinet
    6. 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  crossref  mathscinet
    7. Pulkina L.S., “A nonlocal problem with integral conditions for hyperbolic equation”, Nanosistemy: fizika, khimiya, matematika, 2:4 (2011), 61–70  mathscinet  zmath  elib
    8. Yuandi Wang, Shengzhou Zheng, “The Existence and Behavior of Solutions for Nonlocal Boundary Problems”, Bound Value Probl, 2009 (2009), 1  crossref  mathscinet  isi
    9. Yuandi Wang, “Weak solutions for nonlocal boundary value problems with low regularity data”, Nonlinear Analysis: Theory, Methods & Applications, 67:1 (2007), 103  crossref  mathscinet  zmath
    10. L. A. Muravei, A. V. Filinovskii, “On the non-local boundary-value problem for a parabolic equation”, Math. Notes, 54:4 (1993), 1045–1057  mathnet  crossref  mathscinet  zmath  isi
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    		Математический сборник - 1991 Sbornik: Mathematics
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