Obstruction to the bilinear control of the Gross-Pitaevskii equation: an example with an unbounded potential

摘要

In 1982, Ball, Marsden, and Slemrod proved an obstruction to the controllability of linear dynamics with a bounded bilinear control term. This note presents an example of nonlinear dynamics with respect to the state for which this obstruction still holds while the bilinear control term is not continuous.