Dispersive effects for the Schr\"odinger equation on finite metric graphs with infinite ends
We study the free Schr\"odinger equation on finite metric graphs with infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$ time decay rate at least $t^{-1/2}$. These conditions allow certain metric graphs with circles and/or with commensurable lengths of the bounded ed...
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| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
25.10.2023
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| Subjects | |
| Online Access | Get full text |
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| Abstract | We study the free Schr\"odinger equation on finite metric graphs with
infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$
time decay rate at least $t^{-1/2}$. These conditions allow certain metric
graphs with circles and/or with commensurable lengths of the bounded edges.
Further we study the dynamics of the probability flow between the bounded
sub-graph and the unbounded ends. |
|---|---|
| AbstractList | We study the free Schr\"odinger equation on finite metric graphs with
infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$
time decay rate at least $t^{-1/2}$. These conditions allow certain metric
graphs with circles and/or with commensurable lengths of the bounded edges.
Further we study the dynamics of the probability flow between the bounded
sub-graph and the unbounded ends. |
| Author | Nicaise, Serge Mehmeti, Felix Ali Ammari, Kaïs |
| Author_xml | – sequence: 1 givenname: Felix Ali surname: Mehmeti fullname: Mehmeti, Felix Ali – sequence: 2 givenname: Kaïs surname: Ammari fullname: Ammari, Kaïs – sequence: 3 givenname: Serge surname: Nicaise fullname: Nicaise, Serge |
| BackLink | https://doi.org/10.48550/arXiv.2310.16628$$DView paper in arXiv |
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| Snippet | We study the free Schr\"odinger equation on finite metric graphs with
infinite ends. We give sufficient conditions to obtain the $L^1$ to $L^\infty$
time decay... |
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| SubjectTerms | Mathematics - Analysis of PDEs |
| Title | Dispersive effects for the Schr\"odinger equation on finite metric graphs with infinite ends |
| URI | https://arxiv.org/abs/2310.16628 |
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