Electron. J. Diff. Equ., Vol. 2013 (2013), No. 130, pp. 1-14.

Optimal bilinear control of nonlinear Hartree equation in $\mathbb{R}^3$

Binhua Feng, Jiayin Liu, Jun Zheng

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.

Submitted November 26, 2012. Published May 27, 2013.
Math Subject Classifications: 35Q55, 49J20.
Key Words: Optimal bilinear control problem; nonlinear Hartree equation; compactness; optimal condition.

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Binhua Feng
School of Mathematics and Statistics,Lanzhou University
Lanzhou 730000, China
Tel: +86-0931-8912483; Fax: +86-0931-8912481
email: binhuaf@163.com
Jiayin Liu
School of Mathematics and Statistics, Lanzhou University
Lanzhou 730000, China
email: xecd@163.com
Jun Zheng
Basic Course Department, Emei Campus
Southwest Jiaotong University
Leshan, Sichuan 614202, China
email: zheng123500@sina.com

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