Display Abstract
 Title Two velocity inverse problem on graphs
 Name Victor S Mikhaylov Country Russia Email ftvsm78@gmail.com Co-Author(s) Submit Time 2014-02-26 16:37:43 Session Special Session 75: Differential and difference equations on graphs and their applications
 Contents \begin{document} \begin{center} {\bf Two velocity inverse problem on graphs} \end{center} On a tree-like 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 tree-like networks of elastic strings}, Zeit. Angew. Math. Mech., {\bf 90} (2010), 136--150) 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. \end{document}