Energy decay rates via convexity for some second-order evolution equation with memory and nonlinear time-dependent dissipation

DOI10.1016/j.na.2010.09.007zbMath1213.35116OpenAlexW2086962001MaRDI QIDQ608407

Shun-Tang Wu

Publication date: 25 November 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.09.007

zbMATH Keywords

convexitygeneral decay

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15) Continuation and prolongation of solutions to PDEs (35B60) Abstract hyperbolic equations (35L90) Integro-partial differential equations (35R09)

Related Items (6)

Energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions ⋮ Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term ⋮ General decay and blow-up of solutions for a viscoelastic equation with nonlinear boundary damping-source interactions ⋮ Asymptotic stability and blow up of solutions for a Petrovsky inverse source problem with dissipative boundary condition ⋮ A new general decay result for abstract evolution equation with time-dependent nonlinear dissipation ⋮ Polynomial-exponential stability and blow-up solutions to a nonlinear damped viscoelastic Petrovsky equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Blow-up of positive-initial-energy solutions for an integro-differential equation with nonlinear damping
• General energy decay rates for a weakly damped Timoshenko system
• Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems
• General decay of the solution energy in a viscoelastic equation with a nonlinear source
• General decay estimate of energy for the second order evolution equations with memory
• Viscoelastic relaxation functions compatible with thermodynamics
• Global existence and exponential stability of small solutions to nonlinear viscoelasticity
• Decay rates for viscoelastic plates with memory
• Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping.
• General decay rate estimates for viscoelastic dissipative systems
• Exponential and polynomial decay for a quasilinear viscoelastic equation
• Decay estimates for second order evolution equations with memory
• General decay of solutions of a viscoelastic equation
• Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation
• An abstract Volterra equation with applications to linear viscoelasticity
• Asymptotic stability in viscoelasticity
• Asymptotic behaviour of the energy in partially viscoelastic materials
• Blow up and global existence in a nonlinear viscoelastic wave equation
• A memory type boundary stabilization of a mildly damped wave equation
• Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

This page was built for publication: Energy decay rates via convexity for some second-order evolution equation with memory and nonlinear time-dependent dissipation