On an inverse problem for tree-like networks of elastic strings
Analysis of PDEs
2025-05-29 v1 Spectral Theory
Abstract
We consider the in-plane motion of elastic strings on tree-like network, observed from the 'leaves'. We investigate the inverse problem of recovering not only the physical properties i.e. the 'optical lengths' of each string, but also the topology of the tree which is represented by the edge degrees and the angles between branching edges. To this end use the boundary control method for wave equations established in~\cite{AK,B}. It is shown that under generic assumptions the inverse problem can be solved by applying measurements at all leaves, the root of the tree being fixed.
Cite
@article{arxiv.2505.22115,
title = {On an inverse problem for tree-like networks of elastic strings},
author = {S. A. Avdonin and G. Leugering and V. S. Mikhaylov},
journal= {arXiv preprint arXiv:2505.22115},
year = {2025}
}