Optimal bilinear control of the coupled nonlinear Schrödinger system. (June 2019)

• Record Type: Journal Article
• Authors: Wang, Kai; Zhao, Dun; Feng, Binhua
• Is Part Of: Nonlinear analysis. Volume 47(2019)
• Page Start: 142
• Page End: 167
• Publication Date: 2019-06
• Subjects: Optimal bilinear control -- Coupled nonlinear Schrödinger system -- Fréchet-differentiability -- Optimal condition; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.10.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We investigate the optimal bilinear control problem governed by the coupled nonlinear Schrödinger systems with Coulombian potential in R 3 . The existence of the optimal control with initial data in H 1 is presented by weak convergence method, and the Fréchet-differentiability of the objective functional with respect to the control is obtained based on H 2 regularity. Furthermore, the first-order optimality system is rigorously derived. Our results have improved some recent works.