On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type

DOI10.1023/B:CMAJ.0000027233.69345.cfzbMath1011.35096OpenAlexW2094063440MaRDI QIDQ4800807

Jeong Ja Bae, Jong Yeoul Park

Publication date: 3 April 2003

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/30744

zbMATH Keywords

Galerkin methodexistence and uniqueness

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (6)

Blow-up for a non-degenerate non-local quasilinear wave equation on IR^N ⋮ On uniform decay for transmission problem of Kirchhoff type viscoelastic wave equation ⋮ On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary ⋮ A blow-up result for Kirchhoff-type equations with high energy ⋮ Dynamic properties of a nonlinear viscoelastic Kirchhoff-type equation with acoustic control boundary conditions. I ⋮ DYNAMIC PROPERTIES FOR NONLINEAR VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH ACOUSTIC CONTROL BOUNDARY CONDITIONS Ⅱ

Cites Work

• Asymptotic stability of the bounded or almost periodic solution of the wave equation with nonlinear dissipative term
• Existence and exponential decay for a Kirchhoff-Carrier model with viscosity
• On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms
• Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings
• Non-Linear vibration of an elastic string
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