Global attractor for a nonlinear wave equation arising in elastic waveguide model

DOI10.1016/j.na.2008.02.114zbMath1154.35397OpenAlexW2067377203MaRDI QIDQ1001888

Zhijian Yang

Publication date: 19 February 2009

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.2008.02.114

zbMATH Keywords

global attractordynamical systemnonlinear wave equationinitial boundary value problemlongtime behavior

Mathematics Subject Classification ID

Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (13)

Pointwise estimates of global small solutions to the generalized double dispersion equation ⋮ Existence and asymptotic stability of time periodic solutions to the generalized double dispersion equation with periodic external force ⋮ Asymptotic profile of global solutions to the generalized double dispersion equation via the nonlinear term ⋮ Time periodic solutions to the beam equation with weak damping ⋮ Asymptotic profile of solutions to the linearized double dispersion equation on the half space \(\mathbb{R}^{n}_+\) ⋮ Decay estimate of global solutions to the generalized double dispersion model in Morrey spaces ⋮ A global attractor for the elastic waveguide model in \(\mathbb R^N\) ⋮ Asymptotic profiles of solutions to the generalized double dispersion equation with structural damping ⋮ Global attractor for the generalized double dispersion equation ⋮ Global attractor for a suspension bridge problem with a nonlinear delay term in the internal feedback ⋮ Asymptotic profile of solutions to the double dispersion equation ⋮ Exponential attractor for the Boussinesq equation with strong damping and clamped boundary condition ⋮ Global existence and optimal time-decay estimates of solutions to the generalized double dispersion equation on the framework of Besov spaces

Cites Work

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• Initial boundary value problem of the generalized cubic double dispersion equation
• Finite dimensional behavior for weakly damped driven Schrödinger equations
• Solitary longitudinal waves in an inhomogeneous nonlinearly elastic rod
• Long time behavior of strongly damped nonlinear wave equations
• A note on the strong convergence towards attractors of damped forced KdV equations
• Infinite-dimensional dynamical systems in mechanics and physics.
• Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term
• Limiting behavior of strongly damped nonlinear wave equations
• Longtime behavior of the Kirchhoff type equation with strong damping on \(\mathbb{R}^N\)
• Global attractors for nonlinear wave equations with nonlinear dissipative terms
• Cauchy problem of the generalized double dispersion equation
• Longtime Behaviour of Strongly Damped Wave Equations, Global Attractors and Their Dimension
• Existence and non-existence of global solutions for a class of non-linear wave equations

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