Controllability for Schrödinger type system with mixed dispersion on compact star graphs

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>