Asymptotic behavior of a nonlinear Kirchhoff type equation with spring boundary conditions

DOI10.1016/j.camwa.2011.08.011zbMath1232.35098OpenAlexW1980943961MaRDI QIDQ662215

Daewook Kim, Il Hyo Jung

Publication date: 21 February 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.08.011

zbMATH Keywords

asymptotic behaviorglobal solutionnonlinear wave equationsFaedo-Galerkin approximationCoriolis forcing termspring boundary conditions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05) Second-order nonlinear hyperbolic equations (35L70) Theoretical approximation in context of PDEs (35A35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Strings (74K05) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (7)

Global existence and uniform decay rates for the semi-linear wave equation with damping and source terms ⋮ Stabilization for the Kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control ⋮ Unnamed Item ⋮ Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary ⋮ Unnamed Item ⋮ Existence and exponential decay of the Dirichlet problem for a nonlinear wave equation with the Balakrishnan-Taylor term ⋮ Unnamed Item

Cites Work

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• Stabilization of the Kirchhoff type wave equation with locally distributed damping
• On local solutions of a middly degenerate hyperbolic equation
• On the nonlinear wave equation \(u_{tt}-B(t,\|u_{x}\|^{2})u_{xx} = f(x,t,u,u_{x},u_{t})\) associated with the mixed homogeneous conditions
• Sharp energy decay estimates for the wave equation with a local degenerate dissipation
• Global existence for the wave equation with nonlinear boundary damping and source terms
• Local solutions for a nonlinear degenerate Hyperbolic equation
• Some nonlinear degenerate wave equations
• ON A CLASS OF QUASILINEAR HYPERBOLIC EQUATIONS
• The initial value problem for a nonlinear semi-infinite string
• Transient behavior analysis of vibrationally controlled nonlinear parabolic systems with Neumann boundary conditions
• Asymptotic behavior analysis of a coupled time-varying system: application to adaptive systems
• Existence and asymptotic stability for the semilinear wave equation with boundary damping and source term
• On the non-linear vibration problem of the elastic string

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