Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions

From MaRDI portal
Publication:1187564

DOI10.1007/BF01182480zbMath0780.93082OpenAlexW4250608538MaRDI QIDQ1187564

Roberto Triggiani, Irena Lasiecka

Publication date: 22 July 1992

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01182480




Related Items

The SMGT equation from the boundary: regularity and stabilizationUniform decay rates for a variable-coefficient structural acoustic model with curved interface on a shallow shellExponential stability of the transmission wave equation with a distributed delay term in the boundary dampingExponential stabilization of wave equation with acoustic boundary conditions and its application to memory‐type boundaryExponential stabilization of the transmission wave equation with dynamical boundary conditions and a delay termEnergy decay for a wave equation of variable coefficients with logarithmic nonlinearity source termInverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusionStabilization of the wave equation through nonlinear Dirichlet actuationStability properties of dissipative evolution equations with nonautonomous and nonlinear dampingExact boundary controllability of the structural acoustic model with variable coefficientsNormal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundaryStability of wave equation with variable coefficients by boundary fractional dissipation lawLongtime behavior of multidimensional wave equation with local Kelvin–Voigt dampingSharp regularity theory for elastic and thermoelastic Kirchhoff equations with free boundary conditionsHeat-wave interaction in 2-3 dimensions: optimal rational decay rateUniform stability for solutions of a structural acoustics PDE model with no added dissipative feedbackUniform stabilization of a variable coefficient wave equation with nonlinear damping and acoustic boundaryStabilization of Euler-Bernoulli plate equation with variable coefficients by nonlinear boundary feedbackUniform stabilization of a shallow shell model with nonlinear boundary feedbacksStabilization of the variable-coefficient structural acoustic model with curved middle surface and delay effects in the structural componentGlobal existence and asymptotic behavior for a mildly degenerate Kirchhoff wave equation with boundary dampingAsymptotics for wave equations with damping only on the dynamical boundaryDecay of solutions of the elastic wave equation with a localized dissipationON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATIONUniform decay rates for full von karman system of dynamic theromelasticity with free boundary conditions and partial boundary dissipationOn the attractor for a semilinear wave equation with variable coefficients and nonlinear boundary dissipationExponential asymptotic stability for the Klein Gordon equation on non-compact Riemannian manifoldsPartial exact controllability for inhomogeneous multidimensional thermoelastic diffusion problemGlobal uniqueness and stability in determining the damping coefficient of an inverse hyperbolic problem with non-homogeneous Dirichlet B.C. through an additional localized Neumann boundary traceGlobal smooth solutions for the quasilinear wave equation with boundary dissipationNonlinear boundary stabilization of the wave equations with variable coefficients and time dependent delayDecay rates of the hyperbolic equation in an exterior domain with half-linear and nonlinear boundary dissipationsBoundary controllability of structural acoustic systems with variable coefficients and curved wallsEnergy decay and periodic solution for the wave equation in an exterior domain with half-linear and nonlinear boundary dissipationsBoundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundaryPolynomial decay of a internal nonlinear damping structurally acoustic models with variable coefficientsStability estimates for ill-posed cauchy problems involving hyperbolic equations and inequalitiesPeriodic optimal control in Hilbert spacePolynomial stability of transmission viscoelastic wave and plate equations on Riemannian manifoldsGlobal stabilization of the Navier-Stokes-voight and the damped nonlinear wave equations by finite number of feedback controllersObserver-based boundary control of the sine-Gordon model energyBoundary stabilization for wave equations with damping only on the nonlinear Wentzell boundaryExact controllability of structural acoustic interactionsBoundary observability and stabilization for Westervelt type wave equations without interior dampingReceding horizon control for the stabilization of the wave equationWell-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interactionStability for the wave equation in an unbounded domain with finite measure and with nonlinearities of arbitrary growthThe Multidimensional Wave Equation with Generalized Acoustic Boundary Conditions I: Strong StabilityThe Multidimensional Wave Equation with Generalized Acoustic Boundary Conditions II: Polynomial StabilityStabilization of the wave equation with a nonlinear delay term in the boundary conditionsThe stability for a one-dimensional wave equation with nonlinear uncertainty on the boundaryUniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditionsExistence of global attractors for a semilinear wave equation with nonlinear boundary dissipation and nonlinear interior and boundary sources with critical exponentsSame decay rate of second order evolution equations with or without delayOn the wave equation with semilinear porous acoustic boundary conditionsStabilization of the damped wave equation with Cauchy-Ventcel boundary conditionsBoundary feedback stabilization of a coupled parabolic-hyperbolic Stokes-Lamé PDE systemInverse problem for structural acoustic interactionInverse problem for a structural acoustic system with variable coefficientsSmall data global existence for a fluid-structure modelUniform stability in structural acoustic models with flexible curved wallsUniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary dampingInverse Problem for a Linearized Jordan–Moore–Gibson–Thompson EquationGlobal attractors for a class of weakly damped wave equations with gradient type nonlinearityLocal solutions for a coupled system of Kirchhoff typeUniform decay rate for the transmission wave equations with variable coefficientsEnergy decay of variable-coefficient wave equation with acoustic boundary conditions and delayEnergy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time-varying delay in the boundary feedbackBoundary stabilization of structural acoustic interactions with interface on a Reissner-Mindlin plateBehaviors of the energy of solutions of the wave equation with damping and external forceExponential decay rate for a wave equation with Dirichlet boundary controlExact controllability for second-order hyperbolic equations with variable coefficient-principal part and first-order termsUnified approach to stabilization of waves on compact surfaces by simultaneous interior and boundary feedbacks of unrestricted growthRational energy decay rate for the wave equation with delay term on the dynamical controlUniform decay rate estimates for the wave equation in an inhomogeneous medium with simultaneous interior and boundary feedbacksSharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equationsStabilization of the wave equation with variable coefficients and a delay in dissipative boundary feedbackBackwards uniqueness of the $C_{0}$-semigroup associated with a parabolic-hyperbolic Stokes-Lamé partial differential equation systemOn a structural acoustic model which incorporates shear and thermal effects in the structural componentStrong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditionsStabilization of the wave equation with finite range Dirichlet boundary feedbackBoundary feedback stabilization of the transmission problem of Naghdi's modelEnergy decay rates for the semilinear wave equation with nonlinear localized damping and source termsOn a structural acoustic model with interface a Reissner--Mindlin plate or a Timoshenko beamWell-posedness for a variable-coefficient wave equation with nonlinear damped acoustic boundary conditionsFinite Dimensionality of the Attractor for a Semilinear Wave Equation with Nonlinear Boundary DissipationRate of decay of solutions of the wave equation with arbitrary localized nonlinear dampingStabilization of a transmission wave/plate equationStabilization of the wave equation by on-off and positive-negative feedbacksGlobal existence and general decay estimates for the viscoelastic equation with acoustic boundary conditionsLinear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control → Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay RatesRecovering of damping coefficients for a system of coupled wave equations with Neumann boundary conditions: uniqueness and stabilityExponential Stabilization of the Wave Equation by Dirichlet Integral FeedbackStabilization of an abstract second order system with application to wave equations under non-collocated control and observationsExact Controllability of Structural Acoustic Interactions with Variable CoefficientsImplications of sharp trace regularity results on boundary stabilization of the system of linear elasticityControlling the motion of charged particles in a vacuum electromagnetic field from the boundaryDecay rates of energy of the 1D damped original nonlinear wave equationUniform stabilization for the coupled semi-linear wave and beam equations with distributed nonlinear feedbackThe exponential tracking and disturbance rejection for the nonlinear wave equation via boundary control without any geometrical conditions on the domainAsymptotic stability of the wave equation on compact surfaces and locally distributed damping-A sharp resultGlobal attractor for a wave equation with nonlinear localized boundary damping and a source term of critical exponentCoupled parabolic–hyperbolic Stokes–Lamé PDE system: limit behaviour of the resolvent operator on the imaginary axisSharp trace regularity for an anisotropic elasticity systemExistence, uniqueness and stabilization for a nonlinear plate system with nonlinear dampingStabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditionsUniform stabilization for a semilinear wave equation with variable coefficients and nonlinear boundary conditionsBoundary stabilization of a thin circular cylindrical shell subject to axisymmetric deformationExponential stabilization of the problem of transmission of wave equation with linear dynamical feedback controlInverse/observability estimates for second-order hyperbolic equations with variable coefficientsBoundary feedback stabilization of a critical nonlinear JMGT equation with Neumann-undissipated part of the boundaryBoundary stabilization of a 3-dimensional structural acoustic modelBoundary feedback stabilization of Naghdi's modelSimultaneous exact/approximate boundary controllability of thermo-elastic plates with variable thermal coefficient and moment controlAsymptotic behaviour of nonlinear structural acoustic interactions with thermal effects on the interfaceOn well-posedness for a free boundary fluid-structure modelBoundary stabilization of wave equations with variable coefficients.



Cites Work