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{\bf Two velocity inverse problem on graphs}
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On a treelike graph we investigate the inverse boundary problem
for a two velocity wave equation which holds on each edge for a
two component vector displacement. Physical parameters of the
graph: the densities and lengths of the edges, and also the
topology of the tree as well as the angles between branching edges
are recovered from the Weyl matrix function.
We extend the approach and results of the paper: (S. Avdonin, G.
Leugering and V. Mikhaylov, {\it On an inverse problem for treelike
networks of elastic strings}, Zeit. Angew. Math. Mech., {\bf 90}
(2010), 136150) to the case of variable velocities. It is shown
that the inverse problem can be uniquely solved by applying
measurements at all, or at all but one, boundary vertices.
This talk is based on a joint work with S. Avdonin, A. Choque Rivero
and G. Leugering.
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