TY  - JOUR
T1  - Optimal Control Problem and Integral Quality Criteria with a Special Gradient Term
AU  - Salmanov, Vugar Ibrahim
PY  - 2025
DA  - August
Y2  - 2025
DO  - 10.55549/epstem.1754735
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 310
EP  - 319
VL  - 34
LA  - en
AB  - The paper deals with the optimal control problem with the full-range integral performance criterionfor the nonlinear Schrödinger equation with the specific gradient summand and the complex potential when theperformance criterion is the full-range integral. Concurrently, the first variation formula of the performancecriterion under consideration and via which the necessary condition is established in the form of a variationinequality is found. This article investigates the differentiability of the optimal control problem for a threedimensional nonlinear no stationary Schrödinger equation with a special gradient term and a real-valuedpotential, when the potential depending on both spatial and time dependence and is sought in the class ofmeasurable bounded functions, and the coefficient in the nonlinear part of the equation is a complex number.Therefore, this work differs from previously studied problems nonlinear Schrödinger equation with a specificgradient term, complex potential and is relevant in its significance and also of scientific interest.
KW  - Schrödinger equation
KW  - Optimal control problem
KW  - Complex potential
CR  - Salmanov, V.I. (2025). Optimal control problem and integral quality criteria with a special gradient term. The Eurasia Proceedings of Science, Technology, Engineering and Mathematics (EPSTEM), 34, 310-319.
UR  - https://doi.org/10.55549/epstem.1754735
L1  - https://dergipark.org.tr/en/download/article-file/5107303
ER  -