Optimal bilinear control of Gross-Pitaevskii equations with Coulombian potentials (Q897822)

The paper aims to extend recent results, which establish the possibility of the application of optimal control to the Gross-Piatevskii equation (GPE), to more general situations. The GPE is set in three dimensions. It includes the central Coulomb potential with a time-dependent coefficient and, possibly, an additional nonsingular potential. The work produces rigorous proofs of the existence and well-posedness of the optimal control for the GPE with both repulsive and attractive signs of the nonlinearity. The existence of the variational derivative of the associated unconstrained functional is proved too.