Identifiability of Spatially-Varying Conductivity from Point Observation as an Inverse Sturm–Liouville Problem

This paper discusses identifiability of the spatially varying parameter α (x) in the heat equation uₜ - (α uₓ )ₓ = f from measurement of u at a single point. The identifiability problem is formulated as an inverse Sturm–Liouville problem for (α y')' + λ y = 0. It is proved that the eigenvalues and the normalizing constants determine the above Sturm–Liouville operator uniquely. Identifiability and nonidentifiability results are obtained for three heat conduction problems.