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
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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Mathematics of the USSR-Sbornik, 1993, 74:1, 219–249
MSC: Primary 35K20, 35B45; Secondary 49J20
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
\by L.~A.~Muravei, A.~V.~Filinovskii
\paper On a~problem with nonlocal boundary condition for a~parabolic equation
\jour Mat. Sb.
\jour Math. USSR-Sb.
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L. A. Muravei, A. V. Filinovskii, “On the non-local boundary-value problem for a parabolic equation”, Math. Notes, 54:4 (1993), 1045–1057
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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
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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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