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In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…

Analysis of PDEs · Mathematics 2011-11-21 Yue Ma

We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result…

Analysis of PDEs · Mathematics 2023-12-18 Xilu Zhu

We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…

Analysis of PDEs · Mathematics 2012-08-14 Alexandru D. Ionescu , Benoit Pausader

We consider long time evolution of small solutions to general multispeed Klein-Gordon systems in 3+1 dimensions. We prove that such solutions are always global and scatter to a linear flow, thus extending previous partial results. The main…

Analysis of PDEs · Mathematics 2016-02-05 Yu Deng

In this thesis we explore S. Klainerman's proof on the global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, as established in his paper from 1985. We consider initial data with…

General Mathematics · Mathematics 2025-01-08 Alessandro Massaad

In this paper we prove global existence and global behavior of solutions to quasilinear wave-Klein-Gordon systems in $\mathbb{R}^{1+2}$ with quadratic nonlinearities satisfying the null condition. We consider small, regular and compactly…

Analysis of PDEs · Mathematics 2023-12-07 Qian Zhang

The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering…

Analysis of PDEs · Mathematics 2012-09-20 Tobias Schottdorf

In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the…

Analysis of PDEs · Mathematics 2023-12-06 Xinyu Cheng

We consider the coupled systems of nonlinear wave and Klein-Gordon equations in two space dimensions with cubic nonlinearity. For this kind of systems, the small data global existence is already known if the cubic nonlinearity satisfies a…

Analysis of PDEs · Mathematics 2022-05-30 Minggang Cheng

The aim of this paper is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small, smooth and mildly decaying at infinity. Some physical models strictly related to…

Analysis of PDEs · Mathematics 2018-10-25 Annalaura Stingo

In this paper we study the global existence and uniqueness of solution for a Klein-Gordon equations system with mixed boundary conditions. Also we analyze the asymptotic behavior of this solution.

Analysis of PDEs · Mathematics 2019-10-24 Cládio O. P. Da Silva , Aldo T. Louredo , Manuel Milla Miranda

We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null…

Analysis of PDEs · Mathematics 2025-11-20 Guocong Shang

We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…

Analysis of PDEs · Mathematics 2014-04-08 Hans Lindblad , Avy Soffer

We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null…

Analysis of PDEs · Mathematics 2012-01-17 Soichiro Katayama

We study the Cauchy problem for systems of cubic nonlinear Klein-Gordon equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and…

Analysis of PDEs · Mathematics 2016-02-11 Donghyun Kim

In this paper we study global nonlinear stability for the Dirac-Klein-Gordon system in two and three space dimensions for small and regular initial data. In the case of two space dimensions, we consider the Dirac-Klein-Gordon system with a…

Analysis of PDEs · Mathematics 2023-03-16 Qian Zhang

We prove global existence and scattering for a class of quadratic Schrodinger equations in dimension 2. The proof relies on the idea of space-time resonance.

Analysis of PDEs · Mathematics 2010-01-29 Pierre Germain , Nader Masmoudi , Jalal Shatah

We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with…

Analysis of PDEs · Mathematics 2025-06-13 Chanjin You

In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…

Analysis of PDEs · Mathematics 2017-12-15 Yue MA

It is well known that for the quasilinear Klein-Gordon equation with quadratic nonlinearity and sufficiently decaying small initial data, there exists a global smooth solution if the space dimensions $d\geq2$. When the initial data are of…

Analysis of PDEs · Mathematics 2026-01-21 Fei Hou , Huicheng Yin
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