Global existence of small solutions for cubic quasilinear Klein-Gordon systems in one space dimension

DOI10.1007/s10114-005-0668-4zbMath1107.35078OpenAlexW2084673478MaRDI QIDQ2508631

Daoyuan Fang, Ru Ying Xue

Publication date: 13 October 2006

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0668-4

zbMATH Keywords

Cauchy problemresonance casenull conditionslinear growth at infinityone space dimension case

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Higher-order hyperbolic systems (35L55) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (6)

A note on a system of cubic nonlinear Klein-Gordon equations in one space dimension ⋮ Global existence, blow-up and asymptotic behavior of solutions for a class of coupled nonlinear Klein-Gordon equations with damping terms ⋮ Multiplicity results of periodic solutions for a coupled system of wave equations ⋮ Periodic solutions to Klein-Gordon systems with linear couplings ⋮ Global existence, asymptotic behavior and blow-up of solutions for coupled Klein-Gordon equations with damping terms ⋮ Global existence and non-existence analyses to a nonlinear Klein-Gordon system with damping terms under positive initial energy

Cites Work

• Unnamed Item
• Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension
• On global small amplitude solutions to systems of cubic nonlinear Klein--Gordon equations with different mass terms in one space dimension
• Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions
• Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1
• Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions
• Normal forms and quadratic nonlinear Klein-Gordon equations

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