Optimal bilinear control of nonlinear Hartree equation in R^3

Abstract

This article concerns with the optimal bilinear control for the nonlinear Hartree equation in $mathbb{R}^3$, which describes the mean-field limit of many-body quantum systems. We show the well-posedness of the problem and the existence of an optimal control. In addition, we derive the first-order optimality system.

Keywords

• Optimal bilinear control problem
• nonlinear Hartree equation
• compactness
• optimal condition