Bounded almost global solutions for non Hamiltonian semi-linear Klein-Gordon equations with radial data on compact revolution hypersurfaces

DOI10.5802/aif.2217zbMath1115.35084OpenAlexW2487345531MaRDI QIDQ877525

Jérémie Szeftel, Jean-Marc Delort

Publication date: 24 April 2007

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2006__56_5_1419_0

zbMATH Keywords

radial hypersurfacessmall radial data

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Propagation of singularities; initial value problems on manifolds (58J47)

Related Items (11)

Normal form for semi-linear Klein-Gordon equations with superquadratic oscillators ⋮ Global solutions for nonlinear Klein-Gordon equations in infinite homogeneous waveguides ⋮ Exponential stability estimate for the derivative nonlinear Schrödinger equation* ⋮ About linearization of infinite-dimensional Hamiltonian systems ⋮ Long-time Sobolev stability for small solutions of quasi-linear Klein-Gordon equations on the circle ⋮ An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS ⋮ Sub-exponential stability for the beam equation ⋮ Almost global existence for the semi-linear Klein-Gordon equation on the circle ⋮ Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds ⋮ Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres ⋮ Super-exponential stability estimate for the nonlinear Schrödinger equation

Cites Work

• Birkhoff normal form for partial differential equations with tame modulus
• Normal forms and global existence of solutions to a class of cubic nonlinear Klein-Gordon equations in one space dimension
• Birkhoff normal form for some nonlinear PDEs
• Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations
• 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
• Long-time existence for semi-linear Klein-Gordon equations with small Cauchy data on Zoll manifolds
• Normal forms and quadratic nonlinear Klein-Gordon equations
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