On the inverse problem of the two-velocity tree-like graph
Avdonin S, Abdon CR, Leugering G, Mikhaylov V (2015)
Publication Status: Published
Publication Type: Journal article
Publication year: 2015
Journal
Publisher: Wiley-VCH Verlag
Book Volume: 95
Pages Range: 1490-1500
Journal Issue: 12
Abstract
In this article the authors continue the discussion in [9] about inverse problems for second order elliptic and hyperbolic equations on metric trees from boundary measurements. In the present paper we prove the identifiability of varying densities of a planar tree-like network of strings along with the complete information on the graph, i.e. the lengths of the edges, the edge degrees and the angles between neighbouring edges. The results are achieved using the Titchmarch-Weyl function for the spectral problem and the Steklov-Poincare operator for the dynamic wave equation on the tree. The general result is obtained by a peeling argument which reduces the inverse problem layer-by-layer from the leaves to the clamped root of the tree. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Authors with CRIS profile
Additional Organisation(s)
Involved external institutions
Russian Academy of Sciences / Росси́йская акаде́мия нау́к (RAS)
Russian Federation (RU)
Universidad Michoacana de San Nicolás de Hidalgo (UMSNH)
Mexico (MX)
University of Alaska Fairbanks
United States (USA) (US)
Russian Federation (RU)
Universidad Michoacana de San Nicolás de Hidalgo (UMSNH)
Mexico (MX)
University of Alaska Fairbanks
United States (USA) (US)
How to cite
APA:
Avdonin, S., Abdon, C.R., Leugering, G., & Mikhaylov, V. (2015). On the inverse problem of the two-velocity tree-like graph. ZAMM - Zeitschrift für angewandte Mathematik und Mechanik, 95(12), 1490-1500. https://doi.org/10.1002/zamm.201400126
MLA:
Avdonin, Sergei, et al. "On the inverse problem of the two-velocity tree-like graph." ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 95.12 (2015): 1490-1500.
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