Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions
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Publication:1659613
DOI10.3934/cpaa.2018076zbMath1397.35154arXiv1703.04888OpenAlexW2596159276MaRDI QIDQ1659613
Satoshi Masaki, Jun-Ichi Segata
Publication date: 22 August 2018
Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1703.04888
asymptotic behaviornonlinear Klein-Gordon equationscattering problemmodified scatteringfinal data problem
Asymptotic behavior of solutions to PDEs (35B40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Second-order semilinear hyperbolic equations (35L71)
Related Items
On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension ⋮ Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions ⋮ Scattering for the mass-critical nonlinear Klein-Gordon equations in three and higher dimensions ⋮ The scattering problem for the three-dimensional cubic nonlinear Klein-Gordon equation with rapidly decreasing input data
Cites Work
- Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance
- Nonlinear small data scattering for the wave and Klein-Gordon equation
- Long-range scattering for nonlinear Schrödinger equations in one and two space dimensions.
- 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.
- Low energy scttering for nonlinear Klein-Gordon equations
- Existence of solutions for Schrödinger evolution equations
- \(L^p-L^q\) estimates for the Klein-Gordon equation
- Nonlinear scattering theory at low energy
- Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension \(n\geq{}2\)
- On the asymptotic behavior of solutions of semi-linear wave equations
- 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
- Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation
- Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions
- A note on global existence of solutions to nonlinear Klein-Gordon equations in one space dimension
- Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions
- A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation
- Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions
- 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
- A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions
- Final state problem for the cubic nonlinear Klein–Gordon equation
- SCATTERING OPERATOR FOR NONLINEAR KLEIN–GORDON EQUATIONS
- Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions
- Normal forms and quadratic nonlinear Klein-Gordon equations
- Decay estimates for the Klein ndesh Gordon equation
- Endpoint Strichartz estimates
- Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation
- WAVE OPERATORS FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A NONLINEARITY OF LOW DEGREE IN ONE OR TWO SPACE DIMENSIONS
- Long Range Scattering for Nonlinear Schrödinger Equations with Critical Homogeneous Nonlinearity
- Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions
- A REMARK ON LONG RANGE SCATTERING FOR THE NONLINEAR KLEIN–GORDON EQUATION
- On the Asymptotic Behavior of Nonlinear Wave Equations
