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
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.
inverse problem, overdetermination condition, second order parabolic equation, initial-boundary value problem.
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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
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\paper The inverse problem of recovering a leading coefficient in the two-dimensional heat equation
\jour Mathematical notes of NEFU
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