Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities

DOI10.1016/j.na.2013.11.025zbMath1284.35070arXiv1307.7890OpenAlexW2964280563MaRDI QIDQ2438991

Hideaki Sunagawa, Donghyun Kim

Publication date: 7 March 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.7890

zbMATH Keywords

one space dimensionnonlinear dissipationsmall amplitude solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial value problems for second-order hyperbolic equations (35L15) Second-order semilinear hyperbolic equations (35L71)

Related Items (10)

Large time behavior of solutions to the critical dissipative nonlinear Schrödinger equation with large data ⋮ The initial value problem for nonlinear Schrödinger equations with a dissipative nonlinearity in one space dimension ⋮ On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension ⋮ A note on a system of cubic nonlinear Klein-Gordon equations in one space dimension ⋮ \(L^2\)-decay rate for special solutions to critical dissipative nonlinear Schrödinger equations ⋮ Existence and asymptotic behavior of solutions for a Klein–Gordon system ⋮ Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions ⋮ A note on decay rates of solutions to a system of cubic nonlinear Schrödinger equations in one space dimension ⋮ On Agemi-type structural conditions for a system of semilinear wave equations ⋮ Lower bound estimate for the dissipative nonlinear Schrödinger equation

Cites Work

• The initial value problem for the cubic nonlinear Klein-Gordon equation
• Remarks on the asymptotic behavior of the cubic nonlinear Klein-Gordon equations in one space dimension.
• Lectures on nonlinear hyperbolic differential equations
• 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
• Large time asymptotics of solutions to nonlinear Klein-Gordon systems
• A note on global existence of solutions to nonlinear Klein-Gordon equations in one space dimension
• A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation
• Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms
• “Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1” [Ann. Sci. École Norm. Sup. (4) 34 (1) (2001) 1–61]
• Final state problem for the cubic nonlinear Klein–Gordon equation
• A REMARK ON LONG RANGE SCATTERING FOR THE NONLINEAR KLEIN–GORDON EQUATION

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