Abstract
In this paper, we consider an optimal bilinear control problem for the Gross–Pitaevskii equations with Coulombian potentials. We show the well-posedness of the problem and the existence of an optimal control. In addition, the first order optimality system is rigorously derived. In particular, we prove the Fréchet-differentiability of the unconstrained functional. We extend the study of Hintermüller et al. (2013) [15] to more general power nonlinearities and unbounded potentials.
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