Display Abstract

Title Two velocity inverse problem on graphs

Name Victor S Mikhaylov
Country Russia
Email ftvsm78@gmail.com
Submit Time 2014-02-26 16:37:43
Special Session 75: Differential and difference equations on graphs and their applications
\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}