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Local exact controllability of the 1D nonlinear Schrödinger equation in the case of Dirichlet boundary conditions
Alessandro Duca, Vahagn Nersesyan
We consider the 1D nonlinear Schrödinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground st…
Bilinear control and growth of Sobolev norms for the nonlinear Schrödinger equation
Alessandro Duca, Vahagn Nersesyan
We consider the nonlinear Schrödinger equation (NLS) on a torus of arbitrary dimension. The equation is studied in presence of an external potential field whose time-dependent ampl…
Well-posedness and exponential decay for the Euler-Bernoulli beam conveying fluid equation with non-constant velocity and dynamical boundary conditions
Akram Ben Aissa, Mama Abdelli, Alessandro Duca
In this paper, we consider an Euler-Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving with non-constant velocity and dynamical boundary c…
Controllability of periodic bilinear quantum systems on infinite graphs
Kaïs Ammari, Alessandro Duca
In this work, we study the controllability of the bilinear Schrödinger equation on infinite graphs for periodic quantum states. We consider the bilinear Schrödinger equation $i\par…
Controllability of localized quantum states on infinite graphs through bilinear control fields
Kaïs Ammari, Alessandro Duca
In this work, we consider the bilinear Schrödinger equation in the Hilbert space with an infinite graph. The L…