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

Avdonin S, Leugering G, Mikhaylov V (2010)

Publication Type: Journal article

Publication year: 2010

Journal

ZAMM - Zeitschrift für angewandte Mathematik und Mechanik Wiley-VCH Verlag

Publisher: Wiley-VCH Verlag

Book Volume: 90

Pages Range: 136--150

Volume: 90

Issue: 2

Journal Issue: 2

DOI: 10.1002/zamm.200900295

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 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.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Additional Organisation(s)

Exzellenz-Cluster Engineering of Advanced Materials

Involved external institutions

University of Alaska Fairbanks US United States (USA) (US)

How to cite

APA:

Avdonin, S., Leugering, G., & Mikhaylov, V. (2010). On an inverse problem for tree-like networks of elastic strings. ZAMM - Zeitschrift für angewandte Mathematik und Mechanik, 90(2), 136--150. https://dx.doi.org/10.1002/zamm.200900295

MLA:

Avdonin, Sergei, Günter Leugering, and Victor Mikhaylov. "On an inverse problem for tree-like networks of elastic strings." ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 90.2 (2010): 136--150.

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