On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials
From MaRDI portal
Publication:2475783
DOI10.1016/j.anihpc.2006.07.005zbMath1248.93031OpenAlexW2096818010MaRDI QIDQ2475783
Thomas Duyckaerts, Enrique Zuazua, Zhang, X.
Publication date: 11 March 2008
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/78781
potentialheat equationwave equationoptimalityobservability inequalityCarleman inequalitydecay at infinityMeshkov's construction
Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Observability (93B07)
Related Items
Exact boundary controllability for a coupled system of wave equations with Neumann boundary controls ⋮ Exact observability conditions for Hilbert space dynamical systems connected with Riesz basis of divided differences ⋮ Semiglobal exponential stabilization of nonautonomous semilinear parabolic-like systems ⋮ Feedback boundary stabilization to trajectories for 3D Navier-Stokes equations ⋮ Null controllability for the parabolic equation with a complex principal part ⋮ A Lipschitz stable reconstruction formula for the inverse problem for the wave equation ⋮ Estimates for the controls of the wave equation with a potential ⋮ Exact boundary observability for nonautonomous quasilinear wave equations ⋮ Sharp exponential decay for solutions of the stationary perturbed Dirac equation ⋮ The reflection principle in the control problem of the heat equation ⋮ Sharp observability estimates for a system of two coupled nonconservative hyperbolic equations ⋮ Stabilization to trajectories for parabolic equations ⋮ Analytic properties of heat equation solutions and reachable sets ⋮ Interior control of waves on time dependent domains ⋮ Exponential decay for the semilinear wave equation with localized frictional and Kelvin–Voigt dissipating mechanisms ⋮ Spectral controllability of some singular hyperbolic equations on networks ⋮ Controllability of impulse controlled systems of heat equations coupled by constant matrices ⋮ Hierarchic control for the wave equation ⋮ Recent progress on controllability/observability for systems governed by partial differential equations ⋮ Quantitative uniqueness of solutions to parabolic equations ⋮ Observability inequality for the Kirchhoff-Rayleigh plate like equation in a short time ⋮ Observability Estimate for the Wave Equation with Variable Coefficients ⋮ Controllability of the wave equation with bilinear controls ⋮ Non-localization of eigenfunctions for Sturm-Liouville operators and applications ⋮ Multiplicative controllability of semilinear parabolic equations with Neumann boundary conditions ⋮ Global Carleman Estimate and State Observation Problem for Ginzburg–Landau Equation ⋮ Existence of solution and uniform decay for a contact problem in laminated beam ⋮ Carleman estimate and null controllability for a degenerate parabolic equation with a slightly superlinear reaction term ⋮ Constructive exact control of semilinear 1D heat equations ⋮ Hierarchical exact controllability of hyperbolic equations and Dunford-Pettis' theorem ⋮ Longtime behavior of the hyperbolic equations with an arbitrary internal damping ⋮ Explicit exponential stabilization of nonautonomous linear parabolic-like systems by a finite number of internal actuators ⋮ Carleman estimates and simultaneous boundary controllability of uncoupled wave equations ⋮ Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory ⋮ Exact synchronization by groups for a coupled system of wave equations with Dirichlet boundary controls ⋮ An observability estimate for parabolic equations from a measurable set in time and its applications ⋮ Bang-bang principle of time optimal controls and null controllability of fractional order parabolic equations ⋮ Locally distributed desensitizing controls for the wave equation ⋮ Exact controllability of semilinear heat equations through a constructive approach ⋮ Sharp Observability Inequalities for Hyperbolic Systems with Potentials ⋮ Observability inequality from measurable sets and the shape design problem for stochastic parabolic equations ⋮ Uniform decay rate estimates for the 2D wave equation posed in an inhomogeneous medium with exponential growth source term, locally distributed nonlinear dissipation, and dynamic Cauchy–Ventcel–type boundary conditions ⋮ Stabilization of a semilinear wave equation with delay ⋮ Control theory of stochastic distributed parameter systems: recent progress and open problems ⋮ Determining a nonlinear hyperbolic system with unknown sources and nonlinearity ⋮ A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations ⋮ Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation ⋮ Stability for Semilinear Wave Equation in an Inhomogeneous Medium with Frictional Localized Damping and Acoustic Boundary Conditions ⋮ Null controllability of viscous Hamilton-Jacobi equations ⋮ Null controllability of Grushin-type operators in dimension two ⋮ Insensitizing controls for a class of quasilinear parabolic equations ⋮ Potential well and exact boundary controllability for radial semilinear wave equations on Schwarzschild spacetime ⋮ Sharp estimates and homogenization of the control cost of the heat equation on large domains ⋮ Time optimal control of semilinear parabolic equations via bilinear controls ⋮ An observability estimate for the heat equation from a product of two measurable sets ⋮ Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations ⋮ Simultaneous observability and stabilization of some uncoupled wave equations ⋮ A Fully Discrete Numerical Control Method for the Wave Equation ⋮ Observability Inequalities for the Heat Equation with Bounded Potentials on the Whole Space ⋮ 2\textsc{d} Grushin-type equations: minimal time and null controllable data ⋮ Local null controllability of a free-boundary problem for the quasi-linear 1D parabolic equation ⋮ Controllability for one-dimensional nonlinear wave equations with degenerate damping ⋮ Desensitizing controls for semilinear wave equations ⋮ Uniform decay rate estimates for the wave equation in an inhomogeneous medium with simultaneous interior and boundary feedbacks ⋮ Quantitative uniqueness of some higher order elliptic equations ⋮ Asymptotic behavior for Petrovsky equation with localized damping ⋮ Simultaneous controllability of some uncoupled semilinear wave equations ⋮ A direct method for the stabilization of some locally damped semilinear wave equations ⋮ Uniform decay of the solution to a wave equation with memory conditions on the boundary ⋮ Exponential stability for a transmission problem of a nonlinear viscoelastic wave equation ⋮ Some controllability results for the 2D Kolmogorov equation ⋮ Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials ⋮ A finite element data assimilation method for the wave equation ⋮ Energy decay rate for a coupled hyperbolic system with nonlinear damping ⋮ Global null-controllability and nonnegative-controllability of slightly superlinear heat equations ⋮ Simultaneous and indirect control of waves: Some recent developments and open problems ⋮ Bang-bang property for time optimal control of semilinear heat equation ⋮ Output feedback stabilization for heat equations with sampled-data controls ⋮ The unique continuation property for second order evolution PDEs ⋮ Logarithmic Decay of Hyperbolic Equations with Arbitrary Small Boundary Damping ⋮ Uniform observability estimates for linear waves ⋮ An internal observability estimate for stochastic hyperbolic equations ⋮ A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations ⋮ Carleman Estimates of Some Stochastic Degenerate Parabolic Equations and Application ⋮ Global Carleman Estimates for Waves and Applications ⋮ Exact controllability for the semilinear Mindlin-Timoshenko system ⋮ Minimal time control of exact synchronization for parabolic systems ⋮ Approximation of null controls for semilinear heat equations using a least-squares approach ⋮ Global existence and asymptotic behavior for a coupled hyperbolic system with localized damping ⋮ Null controllability of semilinear parabolic equations via the bilinear control ⋮ Remarks on the Internal Exponential Stabilization to a Nonstationary Solution for 1D Burgers Equations ⋮ Observation estimate for the heat equations with Neumann boundary conditions via logarithmic convexity ⋮ Decay rate estimates for the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation ⋮ Introduction: On Enrique ⋮ Time optimal controls of semilinear heat equation with switching control ⋮ Weak observability estimates for 1-D wave equations with rough coefficients ⋮ Exponential stability for the 2D wave model with localized memory in a past history framework and nonlinearity of arbitrary growth ⋮ Observability Inequalities from Measurable Sets for Some Abstract Evolution Equations ⋮ Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A pointwise lower bound for positive solutions of a Schrödinger equation in \(\mathbb{R}^ N\)
- Uniqueness and non-uniqueness in the Cauchy problem
- Unicité forte à partir d'une variété de dimension quelconque pour des inégalités différentielles elliptiques
- On exact boundary zero-controllability of two-dimensional Navier-Stokes equations
- Null and approximate controllability for weakly blowing up semilinear heat equations
- One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms
- Exact controllability for semilinear wave equations in one space dimension
- Lower bounds of decay order of eigenfunctions of second-order elliptic operators
- Concentration and lack of observability of waves in highly heterogeneous media
- Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time
- A counterexample in a unique continuation problem
- A non uniqueness result for operators of principal type
- The ``window problem for series of complex exponentials
- Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
- ON THE POSSIBLE RATE OF DECAY AT INFINITY OF SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
- Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
- Asymptotic decay of the solution of a second-order elliptic equation in an unbounded domain. Applications to the spectral properties of a Hamiltonian
- On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient
- A Unified Boundary Controllability Theory for Hyperbolic and Parabolic Partial Differential Equations
- The cost of approximate controllability for heat equations: The linear case