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On an inverse problem for tree‐like networks of elastic strings
Author(s) -
Avdonin S.,
Leugering G.,
Mikhaylov V.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900295
Subject(s) - inverse , inverse problem , tree (set theory) , string (physics) , boundary (topology) , mathematics , spanning tree , enhanced data rates for gsm evolution , topology (electrical circuits) , combinatorics , mathematical analysis , computer science , geometry , telecommunications , mathematical physics
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 we use the Boundary Control method for wave equations on graphs established in [4, 7]. 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.