Sharp estimates for biorthogonal families to exponential functions associated to complex sequences without gap conditions

DOI10.3934/eect.2023044arXiv2401.17128OpenAlexW3121779079MaRDI QIDQ6192574

Manuel González-Burgos, Lydia Ouaili

Publication date: 13 February 2024

Published in: Evolution Equations and Control Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2401.17128

zbMATH Keywords

moment problemnull controllabilitybiorthogonal familiescontrol costno gap conditionsnon-scalar parabolic systems

Mathematics Subject Classification ID

Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Eigenvalue problems (93B60) Second-order parabolic systems (35K40) PDEs in connection with control and optimization (35Q93)

Related Items (1)

Analysis of non scalar control problems for parabolic systems by the block moment method

Cites Work

• Unnamed Item
• Unnamed Item
• Minimal time for the null controllability of parabolic systems: the effect of the condensation index of complex sequences
• A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems
• Explicit lower bounds for the cost of fast controls for some 1-D parabolic or dispersive equations, and a new lower bound concerning the uniform controllability of the 1-D transport-diffusion equation
• The cost of the control in the case of a minimal time of control: the example of the one-dimensional heat equation
• The cost of controlling weakly degenerate parabolic equations by boundary controls
• The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials
• New phenomena for the null controllability of parabolic systems: minimal time and geometrical dependence
• Internal null-controllability of the \(N\)-dimensional heat equation in cylindrical domains
• Boundary controllability of parabolic coupled equations
• Two results on exact boundary control of parabolic equations
• A lower bound of the norm of the control operator for the heat equation
• Bounds on functions biorthogonal to sets of complex exponentials. Control of damped elastic systems
• Completeness of sets of complex exponentials
• Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time
• The ``window problem for series of complex exponentials
• Analysis of the null controllability of degenerate parabolic systems of Grushin type via the moments method
• Minimal time of null controllability of two parabolic equations
• Boundary controllability of a one-dimensional phase-field system with one control force
• Precise estimates for biorthogonal families under asymptotic gap conditions
• Boundary null-controllability of semi-discrete coupled parabolic systems in some multi-dimensional geometries
• A block moment method to handle spectral condensation phenomenon in parabolic control problems
• Particle supported control of a fluid-particle system
• New blow-up rates for fast controls of Schrödinger and heat equations
• Exact controllability theorems for linear parabolic equations in one space dimension
• Exact controllability to eigensolutions of the bilinear heat equation on compact networks
• On the Cost of Fast Controls for Some Families of Dispersive or Parabolic Equations in One Space Dimension
• On the null-controllability of diffusion equations
• Internal Observability for Coupled Systems of Linear Partial Differential Equations
• Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations
• Single input controllability of a simplified fluid-structure interaction model
• Sharp estimates of the one-dimensional boundary control cost for parabolic systems
• Sharp Estimates of the One-Dimensional Boundary Control Cost for Parabolic Systems and Application to the $N$-Dimensional Boundary Null Controllability in Cylindrical Domains
• Entire Functions and Muntz-Szasz Type Approximation
• Observability for the one-dimensional heat equation
• An introduction to the mathematical theory of inverse problems
• The cost of approximate controllability for heat equations: The linear case

This page was built for publication: Sharp estimates for biorthogonal families to exponential functions associated to complex sequences without gap conditions