Recovery of the Heat Equation on a Star Graph

In this work, we reconstruct the unknown potential of the heat eqnarray on a three-edge compact star graph from observations of its vertices. By separation of variables, the problem is reduced to the related inverse Sturm–Liouville problems. To extract the spectral data from finite time observations...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 18; no. 6
Main Authors Liu, Dai-Quan, Yang, Chuan-Fu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2021
Springer Nature B.V
Subjects
Apexes
Graph theory
Heat recovery
Mathematics
Mathematics and Statistics
Thermodynamics
35K51
Inverse spectral problem
heat eqnarray on a graph
35R30
34B45
35R02
boundary observation
Sturm–Liouville operator
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Summary:In this work, we reconstruct the unknown potential of the heat eqnarray on a three-edge compact star graph from observations of its vertices. By separation of variables, the problem is reduced to the related inverse Sturm–Liouville problems. To extract the spectral data from finite time observations, we shall use Kramer’s sampling theorem and a result of Boumenir and Tuan. Furthermore, using extracted spectral data we can recover the Sturm–Liouville operators with the help of the Gelfand–Levitan theory.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-021-01881-8