A Hankel determinant zero-order principle for source counting in an inverse heat point-source problem (opens in new tab)

This paper studies the identification of an unknown number of stationary point sources in a two-dimensional heat equation from boundary flux measurements. Unlike many reconstruction approaches that assume the number of sources to be known in advance, we develop a determinant-based counting method that extracts this number directly from the measured data. In the unit disk, the Laplace-transformed and normalized boundary flux admits a Fourier mome...