General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms

DOI10.1063/1.3254323zbMath1304.35438OpenAlexW2024714405MaRDI QIDQ3583704

Wenjun Liu

Publication date: 17 August 2010

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3254323

zbMATH Keywords

wave equationsviscoelasticitynonlinear functions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Linear constitutive equations for materials with memory (74D05) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (69)

Global Existence and Uniform Decay of Solutions for a Coupled System of Nonlinear Viscoelastic Wave Equations with Not Necessarily Differentiable Relaxation Functions ⋮ Well-posedness for a class of wave equation with past history and a delay ⋮ Oscillating kernels and arbitrary decays in viscoelasticity ⋮ General decay of energy to a nonlinear viscoelastic two-dimensional beam ⋮ Uniqueness and stability of an inverse problem for a phase field model using data from one component ⋮ Laminated Timoshenko beams with viscoelastic damping ⋮ Global nonexistence for a viscoelastic wave equation with acoustic boundary conditions ⋮ Energy decay of the solution for a weak viscoelastic equation with a time-varying delay ⋮ Arbitrary decays for a viscoelastic equation ⋮ New general decay result for a system of viscoelastic wave equations with past history ⋮ General decay result for nonlinear viscoelastic equations ⋮ Optimal decay rate estimates of a nonlinear viscoelastic Kirchhoff plate ⋮ Decay rate estimates for a class of quasilinear hyperbolic equations with damping terms involving p-Laplacian ⋮ How to deal with nonlinear terms in the nondissipative case ⋮ Unnamed Item ⋮ Viscoelasticity versus nonlinear feedback in plate systems: optimal decay ⋮ A new approach to the stability of an abstract system in the presence of infinite history ⋮ Energy decay of dissipative plate equations with memory-type boundary conditions ⋮ Global existence and asymptotic behaviour for a viscoelastic plate equation with nonlinear damping and logarithmic nonlinearity ⋮ Stability of wave equation with locally viscoelastic damping and nonlinear boundary source ⋮ Global existence and general decay for a weak viscoelastic equation with acoustic boundary conditions and a logarithmic source term ⋮ Global existence, blow-up and optimal decay for a nonlinear viscoelastic equation with nonlinear damping and source term ⋮ Sharp decay rates for a class of nonlinear viscoelastic plate models ⋮ Asymptotic stability for the second order evolution equation with memory ⋮ On the control of a nonlinear system of viscoelastic equations ⋮ On the General Decay for a System of Viscoelastic Wave Equations ⋮ Asymptotic stability for solutions of a coupled system of quasi-linear viscoelastic Kirchhoff plate equations ⋮ On a perturbed kernel in viscoelasticity ⋮ Uniform decay in viscoelasticity for kernels with small non-decreasingness zones ⋮ A general decay result for a viscoelastic equation in the presence of past and finite history memories ⋮ A new class of kernels leading to an arbitrary decay in viscoelasticity ⋮ On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms ⋮ General decay estimates for a Cauchy viscoelastic wave problem ⋮ General decay and blow-up of solutions for a system of viscoelastic equations of Kirchhoff type with strong damping ⋮ Boundary stabilization of a nonlinear viscoelastic equation with interior time-varying delay and nonlinear dissipative boundary feedback ⋮ On a non-dissipative Kirchhoff viscoelastic problem ⋮ Global existence, nonexistence, and decay of solutions for a viscoelastic wave equation with nonlinear boundary damping and source terms ⋮ The control of Timoshenko beams by memory-type boundary conditions ⋮ Note on intrinsic decay rates for abstract wave equations with memory ⋮ General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback ⋮ Lower and upper bounds for the blow-up time of a class of damped fourth-order nonlinear evolution equations ⋮ General and optimal decay for a quasilinear viscoelastic equation ⋮ Viscoelastic plate equation with boundary feedback ⋮ General decay for a viscoelastic wave equation with strong time-dependent delay ⋮ Asymptotic behavior for a nondissipative and nonlinear system of the Kirchhoff viscoelastic type ⋮ Decay rate of a weakly dissipative viscoelastic plate equation with infinite memory ⋮ On the general stability of a viscoelastic wave equation with an integral condition ⋮ General decay and blow-up of solution for a quasilinear viscoelastic problem with nonlinear source ⋮ Optimal energy decay result for nonlinear abstract viscoelastic dissipative systems ⋮ A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation ⋮ Unnamed Item ⋮ General decay properties of abstract linear viscoelasticity ⋮ Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity ⋮ Asymptotic stability for a viscoelastic equation with nonlinear damping and very general type of relaxation functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations ⋮ General decay rate of a weakly dissipative viscoelastic equation with a general damping ⋮ Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping ⋮ Global existence and general decay for a nonlinear viscoelastic equation with nonlinear localized damping and velocity-dependent material density ⋮ General and optimal decay result for a viscoelastic problem with nonlinear boundary feedback ⋮ A general stability result for a nonlinear wave equation with infinite memory ⋮ Arbitrary decays in linear viscoelasticity ⋮ General stability result for viscoelastic wave equations ⋮ DECAY RATES FOR A COUPLED VISCOELASTIC LAMÉ SYSTEM WITH STRONG DAMPING ⋮ Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions ⋮ New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity ⋮ Plate equations with frictional and viscoelastic dampings ⋮ On a class of nonlinear viscoelastic Kirchhoff plates: well-posedness and general decay rates

Cites Work

• Non-existence of global solutions for nonlinear strongly damped hyperbolic systems
• General decay of the solution energy in a viscoelastic equation with a nonlinear source
• On the control of solutions of viscoelastic equations with boundary feedback
• The exponential stabilization of the higher-dimensional linear system of thermoviscoelasticity
• Saddle points and instability of nonlinear hyperbolic equations
• Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Global nonexistence theorems for quasilinear evolution equations with dissipation
• Precise decay rate estimates for time-dependent dissipative systems
• Global nonexistence theorems for a class of evolution equations with dissipation
• General decay rate estimates for viscoelastic dissipative systems
• Global and blow-up solutions for a system of nonlinear hyperbolic equations with dissipative terms
• Existence and uniform decay for a non-linear viscoelastic equation with strong damping
• Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping
• Well-posedness and uniform decay rates for the Klein–Gordon equation with damping term and acoustic boundary conditions
• Frictional versus Viscoelastic Damping in a Semilinear Wave Equation
• Blow up and global existence in a nonlinear viscoelastic wave equation
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Global existence and uniform stability of solutions for a quasilinear viscoelastic problem
• Existence and asymptotic stability for the semilinear wave equation with boundary damping and source term
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations
• General decay of energy for a viscoelastic equation with nonlinear damping
• Global existence and uniform decay for a nonlinear viscoelastic equation with damping

This page was built for publication: General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms