A new method to obtain decay rate estimates for dissipative systems with localized damping
From MaRDI portal
Publication:1300574
zbMath0940.35034MaRDI QIDQ1300574
Publication date: 10 July 2000
Published in: Revista Matemática Complutense (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/44442
initial boundary value problemdissipative wave equationstabilization of the solutionelastodynamic system with locally distributed damping
Stabilization of systems by feedback (93D15) Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) A priori estimates in context of PDEs (35B45)
Related Items
A new method to obtain decay rate estimates for dissipative systems ⋮ Global Existence and Uniform Decay of Solutions for a Coupled System of Nonlinear Viscoelastic Wave Equations with Not Necessarily Differentiable Relaxation Functions ⋮ General decay rate estimates for viscoelastic wave equation with Balakrishnan-Taylor damping ⋮ Asymptotic behavior of a flexible structure with Cattaneo type of thermal effect ⋮ Unified stability analysis for a Volterra integro-differential equation under creation time perspective ⋮ On wave equation: review and recent results ⋮ A unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi-discretized vibrating damped systems ⋮ Indirect stabilization of locally coupled wave-type systems ⋮ Energy decay of solutions for an extensible beam equation with a weak nonlinear dissipation ⋮ Energy decay and periodic solution for the wave equation in an exterior domain with half-linear and nonlinear boundary dissipations ⋮ Uniform stabilization of the damped Cauchy--Ventcel problem with variable coefficients and dynamic boundary conditions ⋮ Boundary stabilisation of the wave equation in the presence of singularities ⋮ Uniform decay for a viscoelastic wave equation with density and time-varying delay in Rn ⋮ Existence and general decay of Balakrishnan-Taylor viscoelastic equation with nonlinear frictional damping and logarithmic source term ⋮ On the existence and stability of a nonlinear wave system with variable exponents ⋮ Exponential decay for the semilinear wave equation with localized frictional and Kelvin–Voigt dissipating mechanisms ⋮ General decay rate estimates and numerical analysis for a transmission problem with locally distributed nonlinear damping ⋮ Analytical and computational results for the decay of solutions of a damped wave equation with variable-exponent nonlinearities ⋮ A class of fourth-order parabolic equations with logarithmic nonlinearity ⋮ Stability for the Mixed Problem Involving the Wave Equation, with Localized Damping, in Unbounded Domains with Finite Measure ⋮ Uniform decay rate estimates for the semilinear wave equation in inhomogeneous medium with locally distributed nonlinear damping ⋮ Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction ⋮ Stability for the wave equation in an unbounded domain with finite measure and with nonlinearities of arbitrary growth ⋮ Unnamed Item ⋮ Stabilization of the wave equation in a polygonal domain with cracks ⋮ General decay rate estimates for viscoelastic wave equation with variable coefficients ⋮ Exponential decay for semilinear wave equation with localized damping in the hyperbolic space ⋮ Viscoelasticity versus nonlinear feedback in plate systems: optimal decay ⋮ General energy decay rates for a weakly damped Timoshenko system ⋮ Energy decay of dissipative plate equations with memory-type boundary conditions ⋮ Well-posedness and decay in a system of hyperbolic and biharmonic-wave equations with variable exponents and weak dampings ⋮ Global existence and blow-up for wave equation of \(p\)-Laplacian type ⋮ Existence and asymptotic stability of solutions for a hyperbolic equation with logarithmic source ⋮ Stability properties of dissipative evolution equations with nonautonomous and nonlinear damping ⋮ Uniform decay estimates for the semi-linear wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic versus frictional dissipative effects ⋮ Stabilization of the damped wave equation with Cauchy-Ventcel boundary conditions ⋮ General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure ⋮ Sharp energy estimates for nonlinearly locally damped PDEs via observability for the associated undamped system ⋮ On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms ⋮ Well-posedness and stability of a hinged plate equation with a localized nonlinear structural damping ⋮ Stabilization of a semilinear wave equation with delay ⋮ A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations ⋮ A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities ⋮ Uniform decay for a plate equation partially dissipative. ⋮ Exponential stability for the wave model with localized memory in a past history framework ⋮ Energy decay rates for von Kármán system with memory and boundary feedback ⋮ A New Method to Obtain Uniform Decay Rates for Multidimensional Wave Equations with Nonlinear Acoustic Boundary Conditions ⋮ Long-term dynamical behavior of the wave model with locally distributed frictional and viscoelastic damping ⋮ Unnamed Item ⋮ Strong lower energy estimates for nonlinearly damped Timoshenko beams and Petrowsky equations ⋮ A general formula for decay rates of nonlinear dissipative systems. ⋮ Unnamed Item ⋮ Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects ⋮ Behaviors of the energy of solutions of the wave equation with damping and external force ⋮ Some remarks on global existence to the Cauchy problem of the wave equation with nonlinear dissipation ⋮ General decay rate estimates for viscoelastic dissipative systems ⋮ Exponential stabilization of the wave equation on hyperbolic spaces with nonlinear locally distributed damping ⋮ Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term ⋮ Asymptotic stability of the viscoelastic equation with variable coefficients and the Balakrishnan-Taylor damping ⋮ Stabilization for the wave equation with variable coefficients and Balakrishnan-Taylor damping ⋮ Unified approach to stabilization of waves on compact surfaces by simultaneous interior and boundary feedbacks of unrestricted growth ⋮ Viscoelastic plate equation with boundary feedback ⋮ Nonlinear damped partial differential equations and their uniform discretizations ⋮ On convexity for energy decay rates of a viscoelastic equation with boundary feedback ⋮ Asymptotic behavior for Petrovsky equation with localized damping ⋮ Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms ⋮ New trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems ⋮ Rate of decay of solutions of the wave equation with arbitrary localized nonlinear damping ⋮ General energy decay rates for a weakly damped wave equation ⋮ Asymptotic stability of the wave equation on compact manifolds and locally distributed damping: A sharp result ⋮ Optimal energy decay result for nonlinear abstract viscoelastic dissipative systems ⋮ General stability of a viscoelastic variable coefficients plate equation with time-varying delay in localized nonlinear internal feedback ⋮ On the stabilization of the Timoshenko system by a weak nonlinear dissipation ⋮ Energy decay of solutions for a variable-coefficient viscoelastic wave equation with a weak nonlinear dissipation ⋮ Uniform decay rates for viscoelastic dissipative systems ⋮ Numerical analysis for the wave equation with locally nonlinear distributed damping ⋮ Unnamed Item ⋮ Energy decay rate for a coupled hyperbolic system with nonlinear damping ⋮ Theoretical and computational results of a wave equation with variable exponent and time-dependent nonlinear damping ⋮ Uniform stability of transmission of wave-plate equations with source on Riemannian manifold ⋮ Decay rates of energy of the 1D damped original nonlinear wave equation ⋮ Stabilization of the transmission wave/plate equation with variable coefficients on \({\mathbb{R}}^n \) ⋮ Uniform stabilization for the coupled semi-linear wave and beam equations with distributed nonlinear feedback ⋮ Weak Input to State Estimates for 2D Damped Wave Equations with Localized and Nonlinear Damping ⋮ Stability for semilinear hyperbolic coupled system with frictional and viscoelastic localized damping ⋮ Viscoelastic versus frictional dissipation in a variable coefficients plate system with time-varying delay ⋮ Asymptotic stability of the wave equation on compact manifolds and locally distributed viscoelastic dissipation ⋮ Asymptotic stability for a strongly coupled Klein-Gordon system in an inhomogeneous medium with locally distributed damping ⋮ Global existence and asymptotic behavior for a coupled hyperbolic system with localized damping ⋮ Classification of blow-up and global existence of solutions to an initial Neumann problem ⋮ Decay rates for a viscoelastic wave equation with Balakrishnan-Taylor and frictional dampings ⋮ Decay rate estimates for the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation ⋮ Precise decay rate estimates for time-dependent dissipative systems ⋮ Exponential stability for the 2D wave model with localized memory in a past history framework and nonlinearity of arbitrary growth ⋮ Lp-asymptotic stability of 1D damped wave equations with localized and linear damping ⋮ Source Reconstruction by Partial Measurements for a Class of Hyperbolic Systems in Cascade ⋮ Exponential stability for the wave equation with degenerate nonlocal weak damping ⋮ Decay estimate and blow-up for a damped wave equation with supercritical sources
