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A partial inverse problem for quantum graphs with a loop

  • Sheng-Yu Guan , Chuan-Fu Yang ORCID logo EMAIL logo und Dong-Jie Wu
Veröffentlicht/Copyright: 8. Oktober 2020

Abstract

We consider the Sturm–Liouville operator on quantum graphs with a loop with the standard matching conditions in the internal vertex and the jump conditions at the boundary vertex. Given the potential on the loop, we try to recover the potential on the boundary edge from the subspectrum. The uniqueness theorem and a constructive algorithm for the solution of this partial inverse problem are provided.

MSC 2010: 34A55; 34B24; 47E05

Award Identifier / Grant number: 11871031

Award Identifier / Grant number: 11611530682

Funding statement: The research work was supported in part by the National Natural Science Foundation of China (11871031 and 11611530682).

Acknowledgements

The authors would like to thank the referees for valuable comments and Professor N. P. Bondarenko for teaching us the course of inverse problems on quantum graphs in 2019. Inspired by this course, we wrote this paper.

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Received: 2020-07-16
Revised: 2020-09-03
Accepted: 2020-09-07
Published Online: 2020-10-08
Published in Print: 2021-08-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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