Exponential stabilization of a viscoelastic wave equation with dynamic boundary conditions

DOI10.1007/s00030-015-0322-5zbMath1321.93054OpenAlexW2058221180MaRDI QIDQ745906

L. Seghour, Ammar Khemmoudj

Publication date: 15 October 2015

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-015-0322-5

zbMATH Keywords

asymptotic stabilityglobal existenceviscoelastic wave equationdynamical boundary conditionsstrongly positive definite kernels

Mathematics Subject Classification ID

Asymptotic stability in control theory (93D20) Second-order nonlinear hyperbolic equations (35L70) Stability theory for integral equations (45M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial value problems for second-order hyperbolic equations (35L15) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (5)

General decay for a wave equation with Wentzell boundary conditions and nonlinear delay terms ⋮ Well-posedness and exponential decay for the Euler-Bernoulli beam conveying fluid equation with non-constant velocity and dynamical boundary conditions ⋮ Stabilisation of a wave equation with localised memory term and boundary frictional damping ⋮ Uniform stabilization for a semilinear wave equation with variable coefficients and nonlinear boundary conditions ⋮ Stabilisation of a viscoelastic beam conveying fluid

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integro-differential equations of hyperbolic type with positive definite kernels
• A new approach to equations with memory
• The Cauchy problem in one-dimensional nonlinear viscoelasticity
• Uniform stabilization of the damped Cauchy--Ventcel problem with variable coefficients and dynamic boundary conditions
• Global solutions to the equation of viscoelasticity with fading memory
• Inverse/observability estimates for second-order hyperbolic equations with variable coefficients
• Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
• Decay estimates for second order evolution equations with memory
• An abstract Volterra equation with applications to linear viscoelasticity
• Asymptotic stability in viscoelasticity
• Existence and uniform decay for a non-linear viscoelastic equation with strong damping
• Polynomial stabiization of the wave equation with Ventcel's boundary conditions
• Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping
• A stability result for a class of nonlinear integrodifferential equations with L¹kernels
• On a Nonlinear Hyperbolic Volterra Equation
• Positive Definite Measures with Applications to a Volterra Equation
• Evolutionary Integral Equations and Applications
• Frictional versus Viscoelastic Damping in a Semilinear Wave Equation
• Asymptotic Stability and Energy Decay Rates for Solutions of the Wave Equation with Memory in a Star-Shaped Domain

This page was built for publication: Exponential stabilization of a viscoelastic wave equation with dynamic boundary conditions