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.
Funding source: National Natural Science Foundation of China
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.
References
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- The 𝑟-𝑑 class predictions in linear mixed models
- Stability results for weak solutions to backward one-dimensional semi-linear parabolic equations with locally Lipschitz source
- Parameter estimation for a chaotic dynamical system with partial observations
- Extract the information from big data with randomly distributed noise
- A data and knowledge driven approach for SPECT using convolutional neural networks and iterative algorithms
- Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame
- A partial inverse problem for quantum graphs with a loop
- Guided image filtering based ℓ0 gradient minimization for limited-angle CT image reconstruction
- Recovery of the time-dependent implied volatility of time fractional Black–Scholes equation using linearization technique
- Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings
- Soliton orthogonal frequency division multiplexing with phase–frequency coding on the base of inverse scattering transform
Artikel in diesem Heft
- Frontmatter
- The 𝑟-𝑑 class predictions in linear mixed models
- Stability results for weak solutions to backward one-dimensional semi-linear parabolic equations with locally Lipschitz source
- Parameter estimation for a chaotic dynamical system with partial observations
- Extract the information from big data with randomly distributed noise
- A data and knowledge driven approach for SPECT using convolutional neural networks and iterative algorithms
- Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame
- A partial inverse problem for quantum graphs with a loop
- Guided image filtering based ℓ0 gradient minimization for limited-angle CT image reconstruction
- Recovery of the time-dependent implied volatility of time fractional Black–Scholes equation using linearization technique
- Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings
- Soliton orthogonal frequency division multiplexing with phase–frequency coding on the base of inverse scattering transform