{"title":"Controllability for Schrödinger type system with mixed dispersion on compact star graphs","authors":"R. A. Capistrano-Filho, M. Cavalcante, F. Gallego","doi":"10.3934/eect.2022019","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In this work we are concerned with solutions to the linear Schrödinger type system with mixed dispersion, the so-called biharmonic Schrödinger 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 <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\mathcal{G} $\\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=\"M2\">\\begin{document}$ T>T_{min} $\\end{document}</tex-math></inline-formula>, with</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> \\begin{document}$ T_{min} = \\sqrt{ \\frac{ \\overline{L} (L^2+\\pi^2)}{\\pi^2\\varepsilon(1- \\overline{L} \\varepsilon)}}, $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>when the couplings and the controls appear only on the Neumann boundary conditions.</p>","PeriodicalId":176362,"journal":{"name":"Evolution Equations & Control Theory","volume":"71 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Evolution Equations & Control Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/eect.2022019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this work we are concerned with solutions to the linear Schrödinger type system with mixed dispersion, the so-called biharmonic Schrödinger equation. Precisely, we are able to prove an exact control property for these solutions with the control in the energy space posed on an oriented star graph structure \begin{document}$ \mathcal{G} $\end{document} for \begin{document}$ T>T_{min} $\end{document}, with
In this work we are concerned with solutions to the linear Schrödinger type system with mixed dispersion, the so-called biharmonic Schrödinger equation. Precisely, we are able to prove an exact control property for these solutions with the control in the energy space posed on an oriented star graph structure \begin{document}$ \mathcal{G} $\end{document} for \begin{document}$ T>T_{min} $\end{document}, with \begin{document}$ T_{min} = \sqrt{ \frac{ \overline{L} (L^2+\pi^2)}{\pi^2\varepsilon(1- \overline{L} \varepsilon)}}, $\end{document} when the couplings and the controls appear only on the Neumann boundary conditions.
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