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

Abstract

This paper discusses identifiability of the spatially varying parameter α(x) in the heat equation uₜ - (αuₓ)ₓ= f from measurement of u at a single point. The identifiability problem is formulated as an inverse Sturm–Liouville problem for (αy′)′ + λy = 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.

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