Non-localization of eigenfunctions for Sturm-Liouville operators and applications
DOI10.1016/j.jde.2017.09.043zbMath1382.49017OpenAlexW2769840057MaRDI QIDQ1686080
Thibault Liard, Pierre Lissy, Yannick Privat
Publication date: 20 December 2017
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2017.09.043
wave equationeigenfunctionscalculus of variationsSturm-Liouville operatorsextremal problemscontrol theory
Controllability (93B05) Sturm-Liouville theory (34B24) Observability (93B07) Eigenvalue problems for linear operators (47A75) Existence theories for optimal control problems involving partial differential equations (49J20) Optimality conditions for problems involving ordinary differential equations (49K15)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Complexity and regularity of maximal energy domains for the wave equation with fixed initial data
- Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains
- Optimal damping of a membrane and topological shape optimization
- Optimal observation of the one-dimensional wave equation
- Optimal design of the damping set for the stabilization of the wave equation
- Relative rearrangement. An estimation tool for boundary problems
- Optimal shape and position of the support for the internal exact control of a string
- Ergodicity and eigenfunctions of the Laplacian
- Rearrangements and convexity of level sets in PDE
- Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire. (Lacunary series and semi-internal control of vibrations of a rectangular plate)
- Ergodic properties of eigenfunctions for the Dirichlet problem
- On a theorem of Ingham
- Exact controllability for semilinear wave equations in one space dimension
- Perturbation theory for linear operators.
- Quantum ergodicity of boundary values of eigenfunctions
- Optimal shape and location of sensors for parabolic equations with random initial data
- How to estimate observability constants of one-dimensional wave equations? Propagation versus spectral methods
- Cross-like internal observability of rectangular membranes
- Optimal location of controllers for the one-dimensional wave equation
- On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials
- Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold
- Variation and optimization of formes. A geometric analysis
- Optimal shape and position of the actuators for the stabilization of a string
- Some trigonometrical inequalities with applications to the theory of series
- Geometrical Structure of Laplacian Eigenfunctions
- Necessary Conditions for Optimal Control of Distributed Parameter Systems
- Control of Wave Processes with Distributed Controls Supported on a Subregion
- Nonharmonic fourier series and the stabilization of distributed semi-linear control systems
- The rate at which energy decays in a damped String
- Fourier Series in Control Theory
- Hilbert's Inequality
- Bouncing Ball Modes and Quantum Chaos
