An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions
In this paper, we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that the so-called delta-prime matching conditions are satisfied at the internal vertices of the graph. Another specific feature of our investigation is that we use only one bo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Vibration |
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| Online Access: | https://www.mdpi.com/2571-631X/3/4/28 |
| _version_ | 1797547601951719424 |
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| author | Sergei Avdonin Julian Edward |
| author_facet | Sergei Avdonin Julian Edward |
| author_sort | Sergei Avdonin |
| collection | DOAJ |
| description | In this paper, we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that the so-called delta-prime matching conditions are satisfied at 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 Neumann-to-Dirichlet map (acting from one boundary vertex to one boundary and all internal vertices) we recover the topology and geometry of the graph together with the coefficients of the equations. |
| first_indexed | 2024-03-10T14:46:24Z |
| format | Article |
| id | doaj.art-02ada2c637c84b5d822b74c3814c4b84 |
| institution | Directory Open Access Journal |
| issn | 2571-631X |
| language | English |
| last_indexed | 2024-03-10T14:46:24Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Vibration |
| spelling | doaj.art-02ada2c637c84b5d822b74c3814c4b842023-11-20T21:17:06ZengMDPI AGVibration2571-631X2020-11-013444846310.3390/vibration3040028An Inverse Problem for Quantum Trees with Delta-Prime Vertex ConditionsSergei Avdonin0Julian Edward1Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775, USADepartment of Mathematics and Statistics, Florida International University, Miami, FL 33199, USAIn this paper, we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that the so-called delta-prime matching conditions are satisfied at 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 Neumann-to-Dirichlet map (acting from one boundary vertex to one boundary and all internal vertices) we recover the topology and geometry of the graph together with the coefficients of the equations.https://www.mdpi.com/2571-631X/3/4/28inverse problemsquantum graphsdelta-prime vertex conditions |
| spellingShingle | Sergei Avdonin Julian Edward An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions Vibration inverse problems quantum graphs delta-prime vertex conditions |
| title | An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions |
| title_full | An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions |
| title_fullStr | An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions |
| title_full_unstemmed | An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions |
| title_short | An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions |
| title_sort | inverse problem for quantum trees with delta prime vertex conditions |
| topic | inverse problems quantum graphs delta-prime vertex conditions |
| url | https://www.mdpi.com/2571-631X/3/4/28 |
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