Optimal bilinear control of Gross-Pitaevskii equations with Coulombian potentials

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 Frechet-differentiability of the unconstrained functional. We extend the study of Hintermuller et al. (2013) [15] to more general power nonlinearities and unbounded potentials. (C) 2015 Elsevier Inc. All rights reserved.

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