On an inverse problem for tree-like networks of elastic strings

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.

References in corpus (3)

• Kirchhoff's Rule for Quantum Wires
• Scattering matrices and Weyl functions
• The boundary control approach to the Titchmarsh-Weyl $m-$function

Cited by in corpus (7)

• On the inverse problem of the two-velocity tree-like graph
• Reconstruction techniques for quantum trees
• On inverse dynamical and spectral problems for the wave and Schrödinger equations on finite trees. The leaf peeling method
• Recovery of a potential on a quantum star graph from Weyl's matrix
• Method for solving inverse spectral problems on quantum star graphs
• Canonical form of $C^{\ast }$-algebra of eikonals related to the metric graph
• Gel'fand's inverse problem for the graph Laplacian