Recovery of a degenerate space-dependent heat capacity

Abstract

We are concerned with the reconstruction of the heat capacity coefficient of a one-dimensional heat equation from a sequence of observations of solutions at a single fixed point. This new direct method reconstructs the principal eigenfunction by extracting its Fourier coefficients from the observations of the solution. The algorithm presented here is an alternative to Krein's inverse spectral theory, minimization and iterative procedures. Error estimates and numerical experiments are presented.