Decay rate of solutions of a wave equation with damping and external force

DOI10.1016/S0362-546X(00)00118-8zbMath0982.35016OpenAlexW2052918316MaRDI QIDQ5947216

Xiaodong Zhu

Publication date: 26 March 2002

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/s0362-546x(00)00118-8

zbMATH Keywords

energy inequalityKirchhoff strings

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) Degenerate hyperbolic equations (35L80)

Related Items (7)

Local asymptotic stability for polyharmonic Kirchhoff systems† ⋮ Behaviors of the energy of solutions of the wave equation with damping and external force ⋮ Decay rate for a class of viscoelasticity equation with nonlinear damping on the boundary ⋮ Decay rate of quasilinear wave equation with viscosity ⋮ Kirchhoff systems with dynamic boundary conditions ⋮ Asymptotic stability for Kirchhoff systems in variable exponent Sobolev spaces ⋮ Energy bounds for some nonstandard problems in partial differential equations.

Cites Work

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• Asymptotic stability for some nonlinear evolution equations of second order with unbounded dissipative terms
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings
• Some nonlinear degenerate wave equations
• Nonlinear perturbations of the kirchhoff equation

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