Lifespan estimates for the semi-linear Klein-Gordon equation with a quadratic potential in dimension one

DOI10.1016/J.JDE.2016.09.009zbMath1356.35146OpenAlexW2518702351MaRDI QIDQ329260

Qidi Zhang

Publication date: 21 October 2016

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

Full work available at URL: https://doi.org/10.1016/j.jde.2016.09.009

zbMATH Keywords

normal formharmonic oscillatorquadratic potentiallong time existencealgebraic nonlinearity

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Second-order semilinear hyperbolic equations (35L71)

Related Items (8)

Global existence for the semi-linear wave/Klein-Gordon equation associated to the harmonic oscillator in low dimensions ⋮ Exponential stability estimate for the derivative nonlinear Schrödinger equation* ⋮ A note on lower bound lifespan estimates for semi-linear wave/Klein-Gordon equations associated with the harmonic oscillator ⋮ Partial normal form for the semilinear Klein-Gordon equation with quadratic potentials and algebraic non-resonant masses ⋮ Almost global existence for the semi-linear Klein-Gordon equation on the circle ⋮ 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

Cites Work

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• Long time existence for the quadratic wave equation associated to the harmonic oscillator
• 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
• Normal forms for semilinear quantum harmonic oscillators
• Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions
• \(L^p\) eigenfunction bounds for the Hermite operator
• Long-Time Existence for Semi-Linear Klein–Gordon Equations with Quadratic Potential
• Normal forms and quadratic nonlinear Klein-Gordon equations
• Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

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