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Mathematical notes of NEFU, 2017, Volume 24, Issue 1, Pages 74–86 (Mi svfu7)  

Mathematics

The inverse problem of recovering a leading coefficient in the two-dimensional heat equation

B. N. Tsybikov

Ugra State University, 16 Chehova St., Khanty-Mansyisk 628012, Russia

Abstract: We consider the inverse problem of recovering a leading coefficient independent of one of the spatial variable $y$ in the two-dimensional heat equation. The overdetermination data is the values of the solution on the cross-section 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, initial-boundary value problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-41-00063


Full text: PDF file (268 kB)
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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 two-dimensional 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 two-dimensional heat equation
\jour Mathematical notes of NEFU
\yr 2017
\vol 24
\issue 1
\pages 74--86
\mathnet{http://mi.mathnet.ru/svfu7}
\elib{https://elibrary.ru/item.asp?id=30353130}


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