Global exact controllability of the bilinear Schroedinger potential type models on compact quantum graphs

Date/heure
21 novembre 2017
10:45 - 11:45

Oratrice ou orateur
Alessandro Duca

Catégorie d'évènement
Séminaire Équations aux Derivées Partielles et Applications (Nancy)

Let us consider the bilinear Schr »{o}dinger equation $ipartia{l}_{t}psi(t)=Apsi(t)+u(t)Bpsi(t)$ in $L^2(G,mathbbC)$ for $G$ a compact quantum graph. We assume $B$ a bounded symmetric operator, $u$ a control function and $ps{i}^0$ is the initial state of the system. The operator $A=-Delta$ is the Laplacian equipped with self-adjoint type boundary conditions into the vertices of the graph. Provided the well-posedness of the equations, we present assumptions on $B$ and on the spectrum of $A$ implying the global exact controllability in suitable subspaces of $mathcalH$. When the previous assumptions fail, we introduce a weaker notion of controllability allows to provide interesting results also when the graph $G$ is a complex structure and we are not able to verify the spectral assumptions for the global exact controllability. »