PORTUGALIAE MATHEMATICA Vol. 63, No. 3, pp. 293325 (2006) 

A bilinear optimal control problem applied to a time dependent HartreeFock equation coupled with classical nuclear dynamicsLucie BaudouinLaboratoire d'Analyse et d'Architecture des Systèmes, LAAS  CNRS7 avenue du Colonel Roche, 31077 Toulouse Cedex 04  FRANCE Abstract: We study a problem of bilinear optimal control for the electronic wave function of an Helium atom by an external time dependent electric field. The behavior of the atom is modeled by the HartreeFock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, corresponding to the motion of the nucleus. We prove the existence of a bilinear optimal control in the case when the position of the nucleus is known and also prove the corresponding optimality condition. Then, we detail the proof of the existence of an optimal control for the coupled system and complete the study giving a formal optimality condition to define the electric control. Keywords: HartreeFock equation; optimal control; optimality condition. Classification (MSC2000): 49J20, 35Q55. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2006 Sociedade Portuguesa de Matemática
