Almost global existence for the semi-linear Klein-Gordon equation on the circle

DOI10.1016/j.jde.2016.12.013zbMath1361.35113OpenAlexW2564332898MaRDI QIDQ509741

Qidi Zhang, Zheng Han, Daoyuan Fang

Publication date: 17 February 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.12.013

zbMATH Keywords

normal formslong time existencestructure of the nonlinearity

Mathematics Subject Classification ID

Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Hyperbolic equations on manifolds (58J45) Second-order semilinear hyperbolic equations (35L71)

Related Items (8)

Exponential stability estimate for the derivative nonlinear Schrödinger equation* ⋮ Almost global existence for the Klein-Gordon equation with the Kirchhoff-type nonlinearity ⋮ A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential ⋮ Long time existence results for Hamiltonian nonlinear Klein-Gordon equations on some compact manifolds ⋮ A Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation ⋮ Almost global existence for the fractional Schrödinger equations ⋮ Super-exponential stability estimate for the nonlinear Schrödinger equation ⋮ Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit

Cites Work

• Unnamed Item
• Unnamed Item
• Lifespan estimates for the semi-linear Klein-Gordon equation with a quadratic potential in dimension one
• Birkhoff normal form for partial differential equations with tame modulus
• Bounded almost global solutions for non Hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces
• Long-time existence for semi-linear Klein-Gordon equations on tori
• On long time existence for small solutions of semi-linear Klein-Gordon equations on the torus
• Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations
• Long-time existence for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds
• Long-Time Existence for Semi-Linear Klein–Gordon Equations with Quadratic Potential
• Normal forms and quadratic nonlinear Klein-Gordon equations
• Temps d'existence pour l'equation de Klein-Gordon semi-lineaire a donnees petites periodiques
• Almost global existence for solution of semilinear klein-gordon equations with small weakly decaying cauchy data
• Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres
• Long-time Sobolev stability for small solutions of quasi-linear Klein-Gordon equations on the circle
• Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

This page was built for publication: Almost global existence for the semi-linear Klein-Gordon equation on the circle