AN INVERSE PROBLEM FOR QUANTUM TREES WITH OBSERVATIONS AT INTERIOR VERTICES

In this paper we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that positive masses may be attached to the internal vertices of the graph. Another specific feature of our investigation is that we use only one boundary actuator and one boundary sensor, all other observations being internal. Using the Dirichlet-to-Neumann map (acting from one boundary vertex to one boundary and all internal vertices) we recover the topology and geometry of the graph, the coefficients of the equations and the masses at the vertices.

Automated summary

This paper investigates a non-standard dynamical inverse problem for the wave equation on a metric tree graph, where positive masses can be attached to internal vertices. Using only one boundary actuator and one boundary sensor, along with internal observations, the Dirichlet-to-Neumann map is used to recover the topology and geometry of the graph, coefficients of the equations, and the masses at the vertices.