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

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.