
Mathematics
The inverse problem of recovering a leading coefficient in the twodimensional heat equation
B. N. Tsybikov^{} ^{} Ugra State University, 16 Chehova St., KhantyMansyisk 628012, Russia
Abstract:
We consider the inverse problem of recovering a leading coefficient independent of one of the spatial variable $y$ in the twodimensional heat equation. The overdetermination data is the values of the solution on the crosssection of the domain by the hyperplane $y=0$. The solution is sought in the class of functions whose Fourier image in the variable $y$ is compactly supported in the dual variable. Existence and uniqueness conditions of the solution to this problem in this class are established.
Keywords:
inverse problem, overdetermination condition, second order parabolic equation, initialboundary value problem.
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UDC:
517.95 Received: 28.01.2017
Citation:
B. N. Tsybikov, “The inverse problem of recovering a leading coefficient in the twodimensional heat equation”, Mathematical notes of NEFU, 24:1 (2017), 74–86
Citation in format AMSBIB
\Bibitem{Tsy17}
\by B.~N.~Tsybikov
\paper The inverse problem of recovering a leading coefficient in the twodimensional heat equation
\jour Mathematical notes of NEFU
\yr 2017
\vol 24
\issue 1
\pages 7486
\mathnet{http://mi.mathnet.ru/svfu7}
\elib{https://elibrary.ru/item.asp?id=30353130}
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