Optimal bilinear control of Gross-Pitaevskii equations with Coulombian potentials

DOI10.1016/j.jde.2015.10.026zbMath1333.35252OpenAlexW2184108293MaRDI QIDQ897822

Binhua Feng, Dun Zhao

Publication date: 7 December 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.10.026

zbMATH Keywords

well-posednessoptimalityCoulomb interactionsvariational derivative

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (13)

Optimal bilinear control of nonlinear Hartree equations with singular potentials ⋮ Averaging of the nonlinear Schrödinger equation with highly oscillatory magnetic potentials ⋮ Unnamed Item ⋮ On the bilinear control of the Gross-Pitaevskii equation ⋮ Stability of the Hartree equation with time-dependent coefficients ⋮ Optimal bilinear control of the logarithmic Schrödinger equation ⋮ Optimal Control for Stochastic Nonlinear Schrödinger Equation on Graph ⋮ Optimal nonlinearity control of Schrödinger equation ⋮ Optimal bilinear control of the coupled nonlinear Schrödinger system ⋮ Optical solitons in nematic liquid crystals: model with saturation effects ⋮ Dynamical canonical systems and their explicit solutions ⋮ On the Cauchy problem for the XFEL Schrödinger equation ⋮ Optimal Bilinear Control for the X-Ray Free Electron Laser Schrödinger Equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear Schrödinger equation with time dependent potential
• Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control
• Controllability of a quantum particle in a moving potential well
• A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics
• Well-posedness and sharp uniform decay rates at the \(L_{2}(\Omega)\)-level of the Schrödinger equation with nonlinear boundary dissipation
• Exact boundary controllability of the nonlinear Schrödinger equation
• Stability for the time-dependent Hartree equation with positive energy
• Growth of Sobolev norms and controllability of the Schrödinger equation
• Remarks on convergence of the Feynman path integrals
• Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet control
• A Schrödinger equation with time-oscillating nonlinearity
• Constructive solution of a bilinear optimal control problem for a Schrödinger equation
• Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control
• Optimal Bilinear Control of Gross--Pitaevskii Equations
• Global Controllability and Stabilization for the Nonlinear Schrödinger Equation on Some Compact Manifolds of Dimension 3
• Local Exact Controllability and Stabilizability of the Nonlinear Schrödinger Equation on a Bounded Interval
• Generic Controllability Properties for the Bilinear Schrödinger Equation
• Exact Controllability for the Schrödinger Equation
• Geometric control in the presence of a black box
• Optimal Bilinear Control of an Abstract Schrödinger Equation

This page was built for publication: Optimal bilinear control of Gross-Pitaevskii equations with Coulombian potentials