Stability of an abstract-wave equation with delay and a Kelvin–Voigt damping

DOI10.3233/ASY-151317zbMath1336.35251arXiv1408.6261OpenAlexW2963562890MaRDI QIDQ5744766

Serge Nicaise, Kaïs Ammari, Cristina Pignotti

Publication date: 19 February 2016

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.6261

zbMATH Keywords

exponential stabilityinternal stabilizationfrequency-domain approach

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Partial functional-differential equations (35R10) Abstract hyperbolic equations (35L90)

Related Items (13)

General decay for weak viscoelastic Kirchhoff plate equations with delay boundary conditions ⋮ Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback ⋮ Asymptotic behavior of the linearized compressible barotropic Navier‐Stokes system with a time varying delay term in the boundary or internal feedback ⋮ Spectral analysis and stabilization of one dimensional wave equation with singular potential ⋮ Stability results of a singular local interaction elastic/viscoelastic coupled wave equations with time delay ⋮ Exponential stability result for the wave equation with Kelvin-Voigt damping and past history subject to Wentzell boundary condition and delay term ⋮ Asymptotic stability of a viscoelastic problem with time-varying delay in boundary feedback ⋮ A qualitative study and numerical simulations for a time-delayed dispersive equation ⋮ General decay for a viscoelastic equation with time-varying delay in the boundary feedback condition ⋮ On a Kelvin--Voigt Viscoelastic Wave Equation with Strong Delay ⋮ Rapid exponential stabilisation of linear-KdV equation with long input delay on the left boundary ⋮ Well-posedness and exponential stability of a thermoelastic system with internal delay ⋮ Stability results for an elastic–viscoelastic wave equation with localized Kelvin–Voigt damping and with an internal or boundary time delay

Cites Work

• Feedback stabilization of a class of evolution equations with delay
• Feedback boundary stabilization of wave equations with interior delay
• Ill-posed problems in thermomechanics
• A note on the delayed heat equation: instability with respect to initial data
• Instability of coupled systems with delay
• Boundary feedback stabilization by time delay for one-dimensional wave equations
• On the essential spectrum of partial differential boundary problems
• Stabilization of second order evolution equations with unbounded feedback with delay
• Stability and Instability Results of the Wave Equation with a Delay Term in the Boundary or Internal Feedbacks
• An Example on the Effect of Time Delays in Boundary Feedback Stabilization of Wave Equations
• Not All Feedback Stabilized Hyperbolic Systems are Robust with Respect to Small Time Delays in Their Feedbacks
• Two examples of ill-posedness with respect to time delays revisited

This page was built for publication: Stability of an abstract-wave equation with delay and a Kelvin–Voigt damping