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

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Avdonin S, Leugering G, Mikhaylov V
Zeitschrift: ZAMM - Zeitschrift für angewandte Mathematik und Mechanik
Verlag: Wiley-VCH Verlag
Jahr der Veröffentlichung: 2010
Band: 90
Heftnummer: 2
Seitenbereich: 136--150
ISSN: 0044-2267


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.



FAU-Autoren / FAU-Herausgeber

Leugering, Günter Prof. Dr.
Lehrstuhl für Angewandte Mathematik


Zusätzliche Organisationseinheit(en)
Exzellenz-Cluster Engineering of Advanced Materials


Autor(en) der externen Einrichtung(en)
University of Alaska Fairbanks


Zitierweisen

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.

BibTeX: 

Zuletzt aktualisiert 2018-06-08 um 15:53