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.

中文翻译：

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带有内部顶点观测的量子树的反问题

在本文中，我们考虑了度量树图上波动方程的非标准动力学逆问题。我们假设正质量可能会附加到图的内部顶点。我们调查的另一个特定特征是，我们仅使用一个边界致动器和一个边界传感器，所有其他观察结果都是内部的。使用Dirichlet-to-Neumann贴图（作用于一个边界顶点到一个边界以及所有内部顶点），我们恢复了图的拓扑和几何形状，方程的系数以及顶点处的质量。