7 papers
Convergent realizations of Lie subalgebras
Karine Beauchard, Jérémy Le Borgne, Jérémy Le Borgne +2
It has been known since the seminal work of Guillemin and Sternberg that Lie subalgebras of finite codimension of an arbitrary real or complex Lie algebra can be realized as subalg…
Small-time local control of a Schrödinger equation: a negative and a positive quadratic result
Karine Beauchard, Frédéric Marbach, Thomas Perrin
We study the small-time local controllability (STLC) of a bilinear Schrödinger equation with Neumann boundary conditions near its ground state. We focus on the degenerate case whe…
Control theory and splitting methods
Karine Beauchard, Adrien Busnot Laurent, Frédéric Marbach
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form , wher…
Approximate controllability of a bilinear wave equation and minimum time
Karine Beauchard, Thomas Perrin, Eugenio Pozzoli
We study the global approximate controllability (GAC) of a Klein-Gordon wave equation, posed on the torus of arbitrary dimension , with bilinear c…
Small-time approximate controllability of the logarithmic Schr\''dinger equation
Karine Beauchard, Rémi Carles, Eugenio Pozzoli
We consider Schr{ö}dinger equations with logarithmic nonlinearity and bilinear controls, posed on or . We prove their small-time global -approxim…
Examples of small-time controllable Schrödinger equations
Karine Beauchard, Eugenio Pozzoli
A variety of physically relevant bilinear Schrödinger equations are known to be approximately controllable in large times. There are however examples which are approximately contr…