Semiclassical microlocal normal forms and global solutions of modified one-dimensional KG equations

DOI10.5802/aif.3041zbMath1377.35200OpenAlexW4320167567MaRDI QIDQ507073

Jean-Marc Delort

Publication date: 3 February 2017

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

Full work available at URL: https://doi.org/10.5802/aif.3041

zbMATH Keywords

global existenceKlein-Gordon equationssemiclassical analysissemiclassical pseudodifferential operatorsKlainerman vector fields

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Second-order semilinear hyperbolic equations (35L71)

Related Items (14)

Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes ⋮ Nonexistence of small, odd breathers for a class of nonlinear wave equations ⋮ Global existence and asymptotics for the modified two-dimensional Schrödinger equation in the critical regime ⋮ Global Existence of Small Amplitude Solutions for a Model Quadratic Quasilinear Coupled Wave-Klein-Gordon System in Two Space Dimension, with Mildly Decaying Cauchy Data ⋮ On asymptotic stability of the sine-Gordon kink in the energy space ⋮ Long time solutions for quasilinear Hamiltonian perturbations of Schrödinger and Klein-Gordon equations on tori ⋮ Asymptotic stability of the sine-Gordon kink under odd perturbations ⋮ Global solutions for 1D cubic defocusing dispersive equations: Part I ⋮ Testing by wave packets and modified scattering in nonlinear dispersive pde’s ⋮ Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space ⋮ Global solution to the wave and Klein-Gordon system under null condition in dimension two ⋮ Global existence and asymptotics for quasi-linear one-dimensional Klein-Gordon equations with mildly decaying Cauchy data ⋮ A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models ⋮ On asymptotic stability of nonlinear waves

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