Binhua Feng, Jiayin Liu, Jun Zheng
Abstract:
This article concerns with the optimal bilinear control
for the nonlinear Hartree equation in
, 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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