THE OPTIMAL CONTROL PROBLEM FOR ONE-DIMENSIONAL NONLINEAR SHRODINGER EQUATIONS WITH A SPECIAL GRADIENT TERM-Reference-Cited by-同舟云学术

THE OPTIMAL CONTROL PROBLEM FOR ONE-DIMENSIONAL NONLINEAR SHRODINGER EQUATIONS WITH A SPECIAL GRADIENT TERM

Published:2019 Issue:2 (131) Volume: Page:49-66
ISSN:2706-9699
Container-title:Journal of Numerical and Applied Mathematics
language:
Short-container-title:JNAM

Author:

Yagub G.¹,Ibrahimov N. S.²,Zengin M.¹

Affiliation:

1. Kafkas University

2. Lankaran State University

Abstract

In this paper we consider the optimal control problem for a one-dimensional nonlinear Schrodinger equation with a special gradient term and with a complex coefficient in the nonlinear part, when the quality criterion is a final functional and the controls are quadratically summable functions. In this case, the questions of the correctness of the formulation and the necessary condition for solving the optimal control problem under consideration are investigated. The existence and uniqueness theorem for the solution is proved and a necessary condition is established in the form of a variational inequality. Along with these, a formula is found for the gradient of the considered quality criterion.

Publisher

Taras Shevchenko National University of Kyiv

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