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

DOI: 10.1002/zamm.201400126

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

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://dx.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.

BibTeX: Download