The cost of approximate controllability for heat equations: The linear case
From MaRDI portal
Publication:5954433
zbMath1007.93034MaRDI QIDQ5954433
Enrique Zuazua, Enrique Fernández-Cara
Publication date: 4 February 2002
Published in: Advances in Differential Equations (Search for Journal in Brave)
controllabilityheat equationCarleman estimatesdistributed controlbounded controlscost of controllability
Controllability (93B05) Control/observation systems governed by partial differential equations (93C20) Heat equation (35K05)
Related Items
A Dependence of the Cost of Fast Controls for the Heat Equation on the Support of Initial Datum, Remarks on the Control of Two-Phase Stefan Free-Boundary Problems, Internal Controllability of Parabolic Systems with Star- and Tree-like Couplings, Estimates for the controls of the wave equation with a potential, GLOBAL CARLEMAN ESTIMATES FOR DEGENERATE PARABOLIC OPERATORS WITH APPLICATIONS, Tunneling estimates and approximate controllability for hypoelliptic equations, Stability in \(L^q\)-norm for inverse source parabolic problems, Controllability of linear and semilinear non-diagonalizable parabolic systems, Desensitizing control for the heat equation with respect to domain variations, Optimal Control of Parabolic Equations – A Spectral Calculus Based Approach, Observability and null-controllability for parabolic equations in \(L_p\)-spaces, On null‐controllability of the heat equation on infinite strips and control cost estimate, Exact controllability to the trajectories of the one-phase Stefan problem, On instability mechanisms for inverse problems, Carleman estimate and null controllability for a degenerate parabolic equation with a slightly superlinear reaction term, Constructive exact control of semilinear 1D heat equations, Strong stability of linear parabolic time-optimal control problems, The cost of controlling strongly degenerate parabolic equations, Observability and control of parabolic equations on networks with loops, Unnamed Item, Sharp estimates for biorthogonal families to exponential functions associated to complex sequences without gap conditions, Control theory of stochastic distributed parameter systems: recent progress and open problems, Reachable states for infinite-dimensional linear systems: old and new, Unnamed Item, On the lack of null-controllability of the heat equation on the half-line, Sharp estimates and homogenization of the control cost of the heat equation on large domains, Sufficient Criteria and Sharp Geometric Conditions for Observability in Banach Spaces, Phase portrait control for 1D monostable and bistable reaction–diffusion equations, On the null controllability of parabolic equations with nonlinear memory, A Parabolic Approach to the Control of Opinion Spreading, A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Time-Optimal Control Problems, Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels, Remarks on the Controllability of Some Parabolic Equations and Systems, Null controllability of nonlinear convective heat equations, Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients, Insensitizing controls for a semilinear heat equation, Remarques sur l'observabilité pour l'équation de Laplace, Local null controllability of a two-dimensional fluid-structure interaction problem, Controllability results for the two-dimensional heat equation with mixed boundary conditions using Carleman inequalities: a linear and a semilinear case, FURTIVE POLLUTION FOR A DISCRIMINATING SENTINEL, Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques, Sharp estimates of the one-dimensional boundary control cost for parabolic systems, Null controllability of the heat equation in unbounded domains by a finite measure control region, On two methods for quantitative unique continuation results for some nonlocal operators, Null Controllability of Linear Heat and Wave Equations with Nonlocal Spatial Terms, The null controllability for a singular heat equation with variable coefficients, Observability from measurable sets for a parabolic equation involving the Grushin operator and applications, Numerical aspects of large-time optimal control of Burgers equation, Null Controllability of Linear and Semilinear Nonlocal Heat Equations with an Additive Integral Kernel, Perturbations of Time Optimal Control Problems for a Class of Abstract Parabolic Systems, Spectral inequality and optimal cost of controllability for the Stokes system, FURTIVE POLLUTION FOR PARABOLIC EVOLUTION SYSTEM GOVERNED BY CAUCHY PROBLEM, A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations, Logarithmic Decay for Linear Damped Hypoelliptic Wave and Schrödinger Equations, Null controllability of the heat equation with boundary Fourier conditions: the linear case, Unique continuation for stochastic heat equations, Stably determining time-dependent convection–diffusion coefficients from a partial Dirichlet-to-Neumann map, Introduction: On Enrique, Controllability under positive constraints for quasilinear parabolic PDEs, An inverse stability result for non-compactly supported potentials by one arbitrary lateral Neumann observation, On the null controllability of heat equation with memory, Null controllability of a semilinear degenerate parabolic equation with a gradient term, Sparse source identification of linear diffusion-advection equations by adjoint methods, Local null controllability of coupled degenerate systems with nonlocal terms and one control force, Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time, Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient, Stable observation of additive superpositions of partial differential equations, Exact local controllability of a one-control reaction-diffusion system, Global rapid-controllability of a class of semilinear evolution equations, Null controllability for the parabolic equation with a complex principal part, A spectral inequality for degenerate operators and applications, \(L^p\) and \(L^\infty\) norm estimates of the cost of the controllability for heat equations, Null controllability for a fourth order parabolic equation, Local null controllability for degenerate parabolic equations with nonlocal term, Partial null controllability of parabolic linear systems, On the controllability of anomalous diffusions generated by the fractional Laplacian, Internal feedback stabilization of nonstationary solutions to semilinear parabolic systems, Analytic properties of heat equation solutions and reachable sets, Local null-controllability for some quasi-linear phase-field systems with Neumann boundary conditions by one control force, HJB equations in infinite dimensions under weak regularizing properties, Note on the cost of the approximate controllability for the heat equation with potential, Reachability results for perturbed heat equations, About Boltzmann's H theorem for the Landau equation, Uniqueness and reconstruction for the fractional Calderón problem with a single measurement, Quantitative approximation properties for the fractional heat equation, Backward uniqueness results for some parabolic equations in an infinite rod, State observation problem for general time reversible system and applications, Boundary controllability of a one-dimensional phase-field system with one control force, Precise estimates for biorthogonal families under asymptotic gap conditions, Minimal time issues for the observability of Grushin-type equations, Inverse problems for the fourth order Schrödinger equation on a finite domain, Carleman estimates and null controllability of a class of singular parabolic equations, Exact null controllability of KdV-Burgers equation with memory effect systems, Scale-free unique continuation principle for spectral projectors, eigenvalue-lifting and Wegner estimates for random Schrödinger operators, On the controllability of a free-boundary problem for the 1D heat equation, Null controllability for the heat equation with singular inverse-square potentials, A revision of J.-L. Lions' notion of sentinels, A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems, Approximate controllability of a class of semilinear systems with boundary degeneracy, Polynomial decay and control of a 1-d model for fluid-structure interaction., Time optimal controls of the Fitzhugh-Nagumo equation with internal control, On the null controllability of a one-dimensional fluid-solid interaction model., Averaged control and observation of parameter-depending wave equations, The Kalman condition for the boundary controllability of coupled parabolic systems. Bounds on biorthogonal families to complex matrix exponentials, Greedy optimal control for elliptic problems and its application to turnpike problems, Local null controllability for a chemotaxis system of parabolic-elliptic type, Null controllability of nonlinear heat equation with memory effects, On the controllability of the heat equation with nonlinear boundary Fourier conditions., A class of globally controllable semilinear heat equations with superlinear terms, Time optimal controls of the Lengyel-Epstein model with internal control, Observability of the heat equation, geometric constants in control theory, and a conjecture of Luc Miller, On exponential observability estimates for the heat semigroup with explicit rates, Local null controllability of a free-boundary problem for the quasi-linear 1D parabolic equation, New blow-up rates for fast controls of Schrödinger and heat equations, Controllability for a class of reaction-diffusion systems: the generalized Kalman's condition, How violent are fast controls. III., Null controllability of Kolmogorov-type equations, On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials, A new Fourier truncated regularization method for semilinear backward parabolic problems, Internal controllability for parabolic systems involving analytic non-local terms, The cost of controlling weakly degenerate parabolic equations by boundary controls, Carleman estimate for solutions to a degenerate convection-diffusion equation, Well-posedness, blow-up dynamics and controllability of the classical chemotaxis model, Null controllability for a class of degenerate parabolic equations with the gradient terms, Polynomial decay for a hyperbolic-parabolic coupled system, Controllability results for cascade systems of \(m\) coupled parabolic PDEs by one control force, Non-structural controllability of linear elastic systems with structural damping, Sharp observability estimates for heat equations, Exact controllability to the trajectories for parabolic PDEs with nonlocal nonlinearities, Boundary controllability of parabolic coupled equations, Quantitative invertibility and approximation for the truncated Hilbert and Riesz transforms, Controllability of shadow reaction-diffusion systems, Approximate and null controllability for the multidimensional Coleman-Gurtin model, Some controllability results for the 2D Kolmogorov equation, The cost of approximate controllability of heat equation with general dynamical boundary conditions, Output feedback stabilization for heat equations with sampled-data controls, Logarithmic stability in the dynamical inverse problem for the Schrödinger equation by arbitrary boundary observation, Null controllability of the \(N\)-dimensional Stokes system with \(N - 1\) scalar controls, Observation from measurable sets for parabolic analytic evolutions and applications, Quantitative unique continuation for hyperbolic and hypoelliptic equations, Averaged dynamics and control for heat equations with random diffusion, On the boundary controllability of non-scalar parabolic systems, Uniform null controllability of the heat equation with rapidly oscillating periodic density, Controllability and observability of a heat equation with hyperbolic memory kernel, Local null controllability of a 1D Stefan problem, The cost of boundary controllability for a parabolic equation with inverse square potential, Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential, On the local controllability of a class of multidimensional quasilinear parabolic equations, Insensitizing controls of a 1D Stefan problem for the semilinear heat equation, Null and approximate controllability for weakly blowing up semilinear heat equations, On the controllability of a free-boundary problem for 1D heat equation with local and nonlocal nonlinearities, Control of reaction-diffusion models in biology and social sciences, Averaged control, Time optimal controls of semilinear heat equation with switching control, Regional null controllability of linearized Crocco type equation, Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms, Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type, Sparse initial data identification for parabolic PDE and its finite element approximations
