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December  2018, 12(6): 1293-1308. doi: 10.3934/ipi.2018054

## Reconstruction of the coefficients of a star graph from observations of its vertices

 Department of Mathematics, University of West Georgia, GA 30118, USA

Received  December 2016 Revised  March 2018 Published  October 2018

Consider a three-edge star graph, made up of unknown Sturm-Liouville operators on each edge. By using the heat propagation through the graph and measuring the heat transfer occurring at its vertices, we show that we can extract enough spectral data to reconstruct the three Sturm-Liouville operators by using the Gelfand-Levitan theory. Furthermore this reconstruction is achieved by a single measurement provided we use a special initial condition.

Citation: Amin Boumenir, Vu Kim Tuan. Reconstruction of the coefficients of a star graph from observations of its vertices. Inverse Problems & Imaging, 2018, 12 (6) : 1293-1308. doi: 10.3934/ipi.2018054
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