On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary

DOI10.1016/J.NA.2004.11.014zbMath1072.35114OpenAlexW2059363774MaRDI QIDQ1776943

Jeong Ja Bae

Publication date: 12 May 2005

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.2004.11.014

zbMATH Keywords

stabilityKirchhoff equationdecay of the energy

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Partial functional-differential equations (35R10) A priori estimates in context of PDEs (35B45) Higher-order hyperbolic systems (35L55)

Related Items (11)

General decay of solutions of a Bresse system with viscoelastic boundary conditions ⋮ Boundary stabilization of solutions of a nonlinear system of Timoshenko type ⋮ Unnamed Item ⋮ Exact decay rates for weakly coupled systems with indirect damping by fractional memory effects ⋮ Indirect stabilization of a coupled system by memory effects ⋮ On uniform decay for transmission problem of Kirchhoff type viscoelastic wave equation ⋮ Kirchhoff-type system with linear weak damping and logarithmic nonlinearities ⋮ Nonlinear transmission problem for wave equation with boundary condition of memory type ⋮ Unnamed Item ⋮ Global solvability and general decay of a transmission problem for Kirchhoff-type wave equations with nonlinear damping and delay term ⋮ Indirect stabilization on Kirchhoff plates by memory effects

Cites Work

• Unnamed Item
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary.
• Uniform decay of solution for wave equation of Kirchhoff type with nonlinear boundary damping and memory term
• A global existence theorem for the Dirichlet problem in nonlinear \(n\)-dimensional visocelasticity
• Some nonlinear degenerate wave equations
• Quasilinear hyperbolic–hyperbolic singular perturbations with nonmonotone nonlinearity
• Existence and uniform decay of solutions of a degenerate equation with nonlinear boundary damping and boundary memory source term
• Asymptotic Stability and Energy Decay Rates for Solutions of the Wave Equation with Memory in a Star-Shaped Domain
• On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type
• Non-Linear vibration of an elastic string

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