Controllability for Schr\'odinger type system with mixed dispersion on compact star graphs
| Autor: | Capistrano-Filho, Roberto de A., Cavalcante, Márcio, Gallego, Fernando |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Evolution Equations & Control Theory (EECT) 2023 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3934/eect.2022019 |
| Popis: | In this work we are concerned with solutions to the linear Schr\"odinger type system with mixed dispersion, the so-called biharmonic Schr\"odinger equation. Precisely, we are able to prove an exact control property for these solutions with the control in the energy space posed on an oriented star graph structure $\mathcal{G}$ for $T>T_{min}$, with $$T_{min}=\sqrt{ \frac{ \overline{L} (L^2+\pi^2)}{\pi^2\varepsilon(1- \overline{L} \varepsilon)}},$$ when the couplings and the controls appear only on the Neumann boundary conditions. Comment: 15 pages, 1 figure, comments are welcome |
| Databáze: | arXiv |
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