Coupled linear Schrödinger equations: control and stabilization results

DOI10.1007/S00033-024-02242-7MaRDI QIDQ6500161

Sumit Majumdar, Roberto de A. Capistrano-Filho, Kuntal Bhandari, Thiago Yukio Tanaka

Publication date: 10 May 2024

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Mathematics Subject Classification ID

Controllability (93B05) Feedback control (93B52) Initial-boundary value problems for second-order parabolic equations (35K20) Observability (93B07) NLS equations (nonlinear Schrödinger equations) (35Q55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Indirect controllability of locally coupled wave-type systems and applications
• Controllability of cascade coupled systems of multi-dimensional evolution PDEs by a reduced number of controls
• Indirect controllability of locally coupled systems under geometric conditions
• Carleman estimates for the Schrödinger equation and applications to an inverse problem and an observability inequality
• Recent results on the controllability of linear coupled parabolic problems: a survey
• Moving and oblique observations of beams and plates
• On the influence of the coupling on the dynamics of single-observed cascade systems of PDE's
• Rapid exponential stabilization for a linear Korteweg-de Vries equation
• Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems
• Rapid stabilization of a linearized bilinear 1-D Schrödinger equation
• \(L_2(\Sigma)\)-regularity of the boundary to boundary operator \(B^*L\) for hyperbolic and Petrowski PDEs
• How violent are fast controls for Schrödinger and plate vibrations?
• Boundary null-controllability of 1-D coupled parabolic systems with Kirchhoff-type conditions
• Insensitizing exact controls for the scalar wave equation and exact controllability of 2-coupled cascade systems of PDE's by a single control
• Exact controllability of a cascade system of conservative equations
• Controllability of two coupled wave equations on a compact manifold
• Internal control of the Schrödinger equation
• On a system of nonlinear Schrödinger equations with quadratic interaction
• A spectral approach for the exact observability of infinite-dimensional systems with skew-adjoint generator
• Observability and Control of Schrödinger Equations
• Observabilité frontière indirecte de systèmes faiblement couplés
• Rapid Stabilization in a Semigroup Framework
• Internal Controllability of First Order Quasi-linear Hyperbolic Systems with a Reduced Number of Controls
• CONTROL AND STABILIZATION OF THE NONLINEAR SCHRÖDINGER EQUATION ON RECTANGLES
• Simultaneous identification of the diffusion coefficient and the potential for the Schrödinger operator with only one observation
• Local Exact Controllability and Stabilizability of the Nonlinear Schrödinger Equation on a Bounded Interval
• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• A General Theory of Observation and Control
• Rapid Boundary Stabilization of Linear Distributed Systems
• A Two-Level Energy Method for Indirect Boundary Observability and Controllability of Weakly Coupled Hyperbolic Systems
• The Cauchy problem for nonlinear quadratic interactions of the Schrödinger type in one dimensional space
• Fourier Series in Control Theory
• Uniqueness and stability in an inverse problem for the Schr dinger equation
• Periodic pulses of coupled nonlinear Schr\"odinger equations in optics
• Rapid Exponential Feedback Stabilization with Unbounded Control Operators
• Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights
• A Note on Complete Controllability and Stabilizability for Linear Control Systems in Hilbert Space
• Rapid exponential stabilization of a Boussinesq system of KdV–KdV Type
• Carleman estimates and simultaneous boundary controllability of uncoupled wave equations

This page was built for publication: Coupled linear Schrödinger equations: control and stabilization results