scientific article; zbMATH DE number 928680

zbMath0862.49004MaRDI QIDQ4893740

Oleg Yurievich Imanuvilov, Andrei V. Fursikov

Publication date: 22 September 1996

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

optimal controlBurgers equationevolution equationsBoussinesq systemsemilinear parabolic equationsCarleman estimate2-D Navier-Stokes system

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) KdV equations (Korteweg-de Vries equations) (35Q53) Navier-Stokes equations (35Q30) Existence theories for optimal control problems involving partial differential equations (49J20) Initial value problems for linear higher-order PDEs (35G10) Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control (49-02) Higher-order parabolic equations (35K25)

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Application to discriminating sentinels ⋮ Insensitizing controls with two vanishing components for the three-dimensional Boussinesq system ⋮ Carleman Estimates for Some Non-Smooth Anisotropic Media ⋮ Singular Optimal Control for a Transport-Diffusion Equation ⋮ Remarks on the Controllability of Some Parabolic Equations and Systems ⋮ Lipschitz stability in the determination of the principal part of a parabolic equation ⋮ Local null controllability of a two-dimensional fluid-structure interaction problem ⋮ Averaged controllability for random evolution Partial Differential Equations ⋮ Carleman Estimates for Some Two-Dimensional Degenerate Parabolic PDEs and Applications ⋮ FURTIVE POLLUTION FOR A DISCRIMINATING SENTINEL ⋮ A mixed formulation for the direct approximation of \(L^2\)-weighted controls for the linear heat equation ⋮ Null-controllability of one-dimensional parabolic equations ⋮ Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques ⋮ SOME CONTROL RESULTS FOR SIMPLIFIED ONE-DIMENSIONAL MODELS OF FLUID-SOLID INTERACTION ⋮ Null controllability of the heat equation in unbounded domains by a finite measure control region ⋮ Lipschitz Stability in Inverse Source and Inverse Coefficient Problems for a First- and Half-order Time-fractional Diffusion Equation ⋮ Unnamed Item ⋮ Ionic parameters identification of an inverse problem of strongly coupled PDE’s system in cardiac electrophysiology using Carleman estimates ⋮ Local Exact Boundary Controllability for the Compressible Navier--Stokes Equations ⋮ Null-Controllability of Two Species Reaction-Diffusion System with Nonlinear Coupling: A New Duality Method ⋮ Null Controllability of Linear and Semilinear Nonlocal Heat Equations with an Additive Integral Kernel ⋮ Controllability of Coupled Parabolic Systems with Multiple Underactuations, Part 2: Null Controllability ⋮ FURTIVE POLLUTION FOR PARABOLIC EVOLUTION SYSTEM GOVERNED BY CAUCHY PROBLEM ⋮ Carleman Estimates of Some Stochastic Degenerate Parabolic Equations and Application ⋮ On Stability Equivalence between Dynamic Output Feedback and Static Output Feedback for a Class of Second Order Infinite-Dimensional Systems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Degenerate parabolic operators of Kolmogorov type with a geometric control condition ⋮ Boundary null controllability as the limit of internal controllability: The heat case ⋮ Null controllability of the heat equation in pseudo-cylinders by an internal control ⋮ Null Controllability of a Nonlinear Population Dynamics with Age Structuring and Spatial Diffusion ⋮ Null Controllability of a System of Degenerate Nonlinear Coupled Equations Derived from Population Dynamics ⋮ Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates ⋮ Inverse coefficient problem for a magnetohydrodynamics system by Carleman estimates ⋮ Stably determining time-dependent convection–diffusion coefficients from a partial Dirichlet-to-Neumann map ⋮ Null Controllability of the Stabilized Kuramoto--Sivashinsky System with One Distributed Control ⋮ Stackelberg–Nash exact controllability for linear and semilinear parabolic equations ⋮ Controllability of Navier–Stokes Equations ⋮ Observability Inequalities from Measurable Sets for Some Abstract Evolution Equations ⋮ Local controllability of the phase field system ⋮ Stackelberg-Nash null controllability for some linear and semilinear degenerate parabolic equations ⋮ Identification of parameters in ill-posed linear parabolic equations ⋮ Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient ⋮ Lipschitz perturbations of a class of approximately controllable linear systems ⋮ Global rapid-controllability of a class of semilinear evolution equations ⋮ Null-controllability with constraints on the control. ⋮ Local exact controllability of two-phase field solidification systems with few controls ⋮ A spectral inequality for degenerate operators and applications ⋮ Carleman estimate and null controllability of a fourth order parabolic equation in dimension \(N\geq 2\) ⋮ Carleman estimates for elliptic operators with complex coefficients. II: Transmission problems ⋮ Local null controllability for degenerate parabolic equations with nonlocal term ⋮ Finite dimensional null controllability for the semilinear heat equation ⋮ Stabilization to trajectories for parabolic equations ⋮ Approximate controllability of semilinear system with state delay using sequence method ⋮ On the one-dimensional nonlinear monodomain equations with moving controls ⋮ Carleman estimates and controllability results for the one-dimensional heat equation with \(BV\) coefficients ⋮ Null exact controllability of the parabolic equations with equivalued surface boundary condition ⋮ On the controllability of linear parabolic equations with an arbitrary control location for stratified media ⋮ Null controllability of the Burgers system with distributed controls ⋮ Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation ⋮ Estimates of initial conditions of parabolic equations and inequalities in infinite domains via lateral Cauchy data ⋮ Theoretical and numerical local null controllability of a Ladyzhenskaya-Smagorinsky model of turbulence ⋮ Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results ⋮ Local null controllability of a free-boundary problem for the viscous Burgers equation ⋮ Non-null-controllability of the Grushin operator in 2D ⋮ 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 ⋮ Null controllability for some systems of two backward stochastic heat equations with one control force ⋮ Null-controllability of the Kolmogorov equation in the whole phase space ⋮ An observability estimate for parabolic equations from a measurable set in time and its applications ⋮ On the controllability of a free-boundary problem for the 1D heat equation ⋮ Insensitizing controls for the parabolic equation with equivalued surface boundary conditions ⋮ On the theoretical and numerical control of a one-dimensional nonlinear parabolic partial differential equation ⋮ Null controllability of some degenerate wave equations ⋮ Strong convergent approximations of null controls for the 1D heat equation ⋮ Local null controllability of the \(N\)-dimensional Navier-Stokes system with \(N - 1\) scalar controls in an arbitrary control domain ⋮ Insensitizing controls for a large-scale ocean circulation model ⋮ Internal stabilization of semilinear parabolic systems ⋮ Quantification of the unique continuation property for the nonstationary Stokes problem ⋮ Local exact controllability to positive trajectory for parabolic system of chemotaxis ⋮ Null controllability with constraints on the state for stochastic heat equation ⋮ Null controllability of a coupled degenerate system with the first order terms ⋮ Theoretical and numerical local null controllability for a parabolic system with local and nonlocal nonlinearities ⋮ Controllability of a \(4 \times 4\) quadratic reaction-diffusion system ⋮ Boundary feedback stabilization of the Boussinesq system with mixed boundary conditions ⋮ Robust Stackelberg controllability for linear and semilinear heat equations ⋮ On the null controllability of a one-dimensional fluid-solid interaction model. ⋮ The Carleman inequality and its application to periodic optimal control governed by semilinear parabolic differential equations ⋮ Greedy optimal control for elliptic problems and its application to turnpike problems ⋮ Remarks on exact controllability for Stokes and Navier-Stokes systems. ⋮ Null controllability of nonlinear heat equation with memory effects ⋮ Heuristic determination of resolving controls for exact and approximate controllability of nonlinear dynamic systems ⋮ On the controllability of the heat equation with nonlinear boundary Fourier conditions. ⋮ Observability estimate for the fractional order parabolic equations on measurable sets ⋮ An inverse source problem for singular parabolic equations with interior degeneracy ⋮ Robust Stackelberg controllability for the Navier-Stokes equations ⋮ Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustics ⋮ On the boundary controllability of a semilinear degenerate system with the convection term ⋮ Stackelberg-Nash exact controllability for the Kuramoto-Sivashinsky equation ⋮ A global Carleman inequality and exact controllability of parabolic equations with mixed boundary conditions ⋮ Local null controllability of the \(N\)-dimensional Navier-Stokes system with nonlinear Navier-slip boundary conditions and \(N-1\) scalar controls ⋮ Time-varying bang-bang property of time optimal controls for heat equation and its application ⋮ Null controllability of a nonlinear dissipative system and application to the detection of the incomplete parameter for a nonlinear population dynamics model ⋮ Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface ⋮ Quantitative Fattorini-Hautus test and minimal null control time for parabolic problems ⋮ Carleman inequalities for the heat equation in singular domains ⋮ Carleman estimate for solutions to a degenerate convection-diffusion equation ⋮ Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems ⋮ Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations ⋮ Exact controllability to trajectories for a semilinear heat equation with a superlinear nonlinearity ⋮ Local exact controllability of the Navier-Stokes system ⋮ Stability of diffusion coefficients in an inverse problem for the Lotka-Volterra competition system ⋮ Controllability and hedgibility of Black-Scholes equations with \(N\) stocks ⋮ Approximate controllability for linear stochastic differential equations in infinite dimensions ⋮ Boundary controllability of parabolic coupled equations ⋮ Sharp Carleman estimates for singular parabolic equations and application to Lipschitz stability in inverse source problems ⋮ Controllability and observability theory of certain parabolic integrodifferential equations ⋮ Carleman estimates and null controllability for boundary-degenerate parabolic operators ⋮ Exact controllability of nonlinear diffusion equations arising in reactor dynamics ⋮ Null controllability of the complex Ginzburg-Landau equation ⋮ 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 ⋮ Some inverse stability results for the bistable reaction-diffusion equation using Carleman inequalities ⋮ On the boundary controllability of non-scalar parabolic systems ⋮ Uniform null controllability of the heat equation with rapidly oscillating periodic density ⋮ Exact null controllability of a semilinear parabolic equation arising in finance ⋮ On the controllability of the fifth-order Korteweg-de Vries equation ⋮ On the local controllability of a class of multidimensional quasilinear parabolic equations ⋮ A complex-analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit ⋮ Null controllability of semilinear parabolic equations via the bilinear control ⋮ Inverse/observability estimates for second-order hyperbolic equations with variable coefficients ⋮ Null and approximate controllability for weakly blowing up semilinear heat equations ⋮ Simultaneous exact/approximate boundary controllability of thermo-elastic plates with variable thermal coefficient and moment control ⋮ Exact and approximate controllability of the age and space population dynamics structured model ⋮ Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity ⋮ Regional null controllability of linearized Crocco type equation ⋮ Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms ⋮ Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems ⋮ Local internal controllability of the Boussinesq system. ⋮ Carleman estimates for a magnetohydrodynamics system and application to inverse source problems ⋮ Impulse null approximate controllability for heat equation with dynamic boundary conditions ⋮ Exact controllability of a semilinear reaction–diffusion equation governed by a bilinear control ⋮ Local logarithmic stability of an inverse coefficient problem for a singular heat equation with an inverse-square potential ⋮ Hierarchical exact controllability of hyperbolic equations and Dunford-Pettis' theorem ⋮ Controllability and observability for some forward stochastic complex degenerate/singular Ginzburg–Landau equations ⋮ Small-time global null controllability of generalized Burgers’ equations ⋮ Local null controllability of a quasi-linear system and related numerical experiments ⋮ Controllability results for cascade systems of m coupled N-dimensional stokes and Navier-stokes systems by N – 1 scalar controls ⋮ Controllability for degenerate/singular parabolic systems involving memory terms ⋮ Carleman estimates and simultaneous boundary controllability of uncoupled wave equations ⋮ On the exact controllability of a semilinear evolution equation with an unbounded operator ⋮ Cost of observability inequalities for elliptic equations in 2-d with potentials and applications to control theory ⋮ Controllability of a fluid-structure interaction system coupling the Navier-Stokes system and a damped beam equation ⋮ Uniform turnpike property and singular limits ⋮ Null boundary controllability for some biological and chemical diffusion problems ⋮ Remarks on the controllability of parabolic systems with non-diagonalizable diffusion matrix ⋮ On a general degenerate/singular parabolic equation with a nonlocal space term ⋮ Null controllability for stochastic parabolic equations with dynamic boundary conditions ⋮ Control problems for the Navier-Stokes system with nonlocal spatial terms ⋮ Exact and approximate controllability of nonlinear dynamic systems in infinite time: The Green's function approach ⋮ Inverse parabolic problems by Carleman estimates with data taken at initial or final time moment of observation ⋮ A Kalman condition for the controllability of a coupled system of Stokes equations ⋮ Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions ⋮ Null controllability of a nonlinear age, space and two-sex structured population dynamics model ⋮ Controllability of a simplified time-discrete stabilized Kuramoto-Sivashinsky system ⋮ Boundary null controllability for the heat equation with dynamic boundary conditions ⋮ Exact controllability of semilinear heat equations through a constructive approach ⋮ Hierarchical controllability for a nonlinear parabolic equation in one dimension ⋮ Quantitative unique continuation for spectral subspaces of Schrödinger operators with singular potentials ⋮ Existence of controls insensitizing the rotational of the solution of the Navier-Stokes system having a vanishing component ⋮ Observability and control of parabolic equations on networks with loops ⋮ Boundary Controllability for a Degenerate Wave Equation in Nondivergence Form with Drift ⋮ An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation ⋮ Global uniqueness in an inverse problem for a class of damped stochastic plate equations ⋮ Local null controllability of the stabilized Kuramoto-Sivashinsky system using moment method ⋮ Observability inequality from measurable sets and the shape design problem for stochastic parabolic equations ⋮ Null controllability of a retarded population dynamics model with interior degeneracy ⋮ Null controllability and Stackelberg-Nash strategy for a \(2 \times 2\) system of parabolic equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ SIMULTANEOUS NULL-CONTROLLABILITY FOR A TWO STROKE SYSTEM WITH CONSTRAINTS ON THE CONTROL ⋮ Existence of Insensitizing Controls for a Semilinear Heat Equation with a Superlinear Nonlinearity ⋮ A Dependence of the Cost of Fast Controls for the Heat Equation on the Support of Initial Datum ⋮ Carleman Estimates of Refined Stochastic Beam Equations and Applications ⋮ Remarks on the Control of Two-Phase Stefan Free-Boundary Problems ⋮ Internal Controllability of Parabolic Systems with Star- and Tree-like Couplings ⋮ Unnamed Item ⋮ Corrigendum: Recover the source and initial value simultaneously in a parabolic equation (2014 Inverse Problems 30 065013) ⋮ Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations ⋮ GLOBAL CARLEMAN ESTIMATES FOR DEGENERATE PARABOLIC OPERATORS WITH APPLICATIONS ⋮ Uniform Null Controllability for a Degenerating Reaction-Diffusion System Approximating a Simplified Cardiac Model ⋮ Time optimal controls of the Cahn-Hilliard equation with internal control ⋮ Harmonic Analysis and Random Schrödinger Operators ⋮ Null-controllability of hypoelliptic quadratic differential equations ⋮ Local Exact Controllability for the Planar Compressible Magnetohydrodynamic Equations ⋮ Existence of Solutions and Local Null Controllability for a Model of Tissue Invasion by Solid Tumors ⋮ Unnamed Item ⋮ Analyticity of Solutions to Parabolic Evolutions and Applications ⋮ Bilinear local controllability to the trajectories of the Fokker-Planck equation with a localized control ⋮ Desensitizing control for the heat equation with respect to domain variations ⋮ A source reconstruction algorithm for the Stokes system from incomplete velocity measurements ⋮ Local exact controllability for the two- and three-dimensional compressible Navier–Stokes equations ⋮ On uniform controllability of 1D transport equations in the vanishing viscosity limit ⋮ Stackelberg-Nash null controllability for a non linear coupled degenerate parabolic equations ⋮ Null controllability and numerical simulations for a class of degenerate parabolic equations with nonlocal nonlinearities ⋮ Carleman Inequalities for Wave Equations with Oscillatory Boundary Conditions and Application ⋮ Observability Inequalities for Parabolic Equations over Measurable Sets and Some Applications Related to the Bang-Bang Property for Control Problems ⋮ On the local exact controllability of micropolar fluids with few controls ⋮ Unnamed Item ⋮ Null controllability for a structurally damped stochastic plate equation ⋮ Approximation of optimal control problems for the Navier-Stokes equation via multilinear HJB-POD ⋮ Local null-controllability of a system coupling Kuramoto-Sivashinsky-KdV and elliptic equations ⋮ On the lack of null-controllability of the heat equation on the half-line ⋮ Remarks on exact controllability for the Navier-Stokes equations ⋮ Unnamed Item ⋮ Approximate and Exact Controllability of the Continuity Equation with a Localized Vector Field ⋮ Partial Approximate Controllability for Linear Stochastic Control Systems ⋮ On the identification of multiple space dependent ionic parameters in cardiac electrophysiology modelling ⋮ Uniform Controllability of a Stokes Problem with a Transport Term in the Zero-Diffusion Limit ⋮ Observability Inequalities for the Heat Equation with Bounded Potentials on the Whole Space ⋮ Exact controllability of Galerkin’s approximations of micropolar fluids ⋮ Detection-Identification of multiple unknown time-dependent point sources in a 2D transport equation: application to accidental pollution ⋮ Unnamed Item ⋮ On the Reachable Set for the One-Dimensional Heat Equation ⋮ Exact controllability for second-order hyperbolic equations with variable coefficient-principal part and first-order terms ⋮ On the controllability of the Burger equation ⋮ About stability and regularization of ill-posed elliptic Cauchy problems: the case ofC^1,1domains ⋮ Null controllability of nonlinear convective heat equations ⋮ Null Controllability of One-dimensional Parabolic Equations by the Flatness Approach ⋮ Global non-negative controllability of the semilinear parabolic equation governed by bilinear control ⋮ Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients ⋮ Unicité forte à l'infini pour KdV ⋮ Controllability of a Reaction-Diffusion System Describing Predator–Prey Model ⋮ Insensitizing controls for a semilinear heat equation ⋮ Exact controllability of the heat equation with bilinear control ⋮ Exact controllability for the magnetohydrodynamic equations ⋮ Controllability results for the two-dimensional heat equation with mixed boundary conditions using Carleman inequalities: a linear and a semilinear case ⋮ Null-controllability of some systems of parabolic type by one control force ⋮ Control from an interior hypersurface ⋮ Simultaneous and indirect control of waves: Some recent developments and open problems ⋮ An Inverse Source Problem Related to Acoustic Nonlinearity Parameter Imaging ⋮ Logarithmic stability for a coefficient inverse problem of coupled Schrödinger equations ⋮ On the uniform controllability for a family of non-viscous and viscous Burgers-α systems ⋮ The Bang-bang principle of time optimal controls for the Kuramoto-Sivashinsky-KdV equation with internal control ⋮ Null Controllability of Linear Heat and Wave Equations with Nonlocal Spatial Terms ⋮ Determination of a source term in a partial differential equation arising in finance ⋮ NULL CONTROLLABILITY OF DEGENERATE NONAUTONOMOUS PARABOLIC EQUATIONS ⋮ The null controllability for a singular heat equation with variable coefficients ⋮ Interior local null controllability of one‐dimensional compressible flow near a constant steady state ⋮ Observability from measurable sets for a parabolic equation involving the Grushin operator and applications ⋮ Lipschitz Stability in Inverse Source Problems for Singular Parabolic Equations ⋮ Numerical null controllability of the heat equation through a least squares and variational approach ⋮ UNIFORM CONTROLLABILITY OF A TRANSPORT EQUATION IN ZERO DIFFUSION–DISPERSION LIMIT ⋮ On the null-controllability of diffusion equations ⋮ Singular optimal control of a 1-D parabolic-hyperbolic degenerate equation ⋮ Controllability of One-Dimensional Viscous Free Boundary Flows ⋮ Logarithmic Decay for Linear Damped Hypoelliptic Wave and Schrödinger Equations ⋮ Global Carleman Estimates for Waves and Applications ⋮ Null controllability of the heat equation with boundary Fourier conditions: the linear case ⋮ Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case ⋮ Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions ⋮ A penalty approach to the infinite horizon LQR optimal control problem for the linearized Boussinesq system ⋮ Approximation of null controls for semilinear heat equations using a least-squares approach ⋮ Uniform null controllability for parabolic equations with discontinuous diffusion coefficients ⋮ Observability and unique continuation of the adjoint of a linearized simplified compressible fluid-structure model in a 2d channel ⋮ Cost for a controlled linear KdV equation ⋮ Numerical reconstruction based on Carleman estimates of a source term in a reaction–diffusion equation ⋮ Boundary null-controllability of two coupled parabolic equations: simultaneous condensation of eigenvalues and eigenfunctions ⋮ Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity ⋮ On exact controllability for the Navier-Stokes equations ⋮ A non-iterative method for identifying multiple unknown time-dependent sources compactly supported occurring in a 2D parabolic equation ⋮ Optimal control of a stochastic heat equation with boundary-noise and boundary-control ⋮ Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems ⋮ Switching Controls for Analytic Semigroups and Applications to Parabolic Systems ⋮ Heating control of a finite rod with a mobile source ⋮ Null boundary controllability of a one-dimensional heat equation with an internal point mass and variable coefficients ⋮ Stability estimate for the semi-discrete linearized Benjamin-Bona-Mahony equation ⋮ A uniform bound on costs of controlling semilinear heat equations on a sequence of increasing domains and its application ⋮ Null Controllability of a Degenerate Cascade Model in Population Dynamics ⋮ Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls