The identifiability of spatial variable coefficients for the vibrating string and Euler-Bernoulli beam are considered. It is shown that the coefficients can be determined by means of boundary control and observation in a finite time duration. These results can be considered as the generalization of infinite-time coefficients identifiability through the application of the Ingham-Beurling theorem.
"Application of Ingham-Beurling-type theorems to coefficient identifiability of vibrating systems: finite time identifiability." Differential Integral Equations 21 (11-12) 1037 - 1054, 2008. https://doi.org/10.57262/die/1355502293